A rolling bearing with seal ring, comprising: an outer ring that is provided with an outer ring raceway around an inner-circumferential surface thereof; an inner ring that is provided with an inner ring raceway around an outer-circumferential surface thereof, and that is located on-an inner-diameter side of the outer ring so as to be concentric with the outer ring; a plurality of rolling bodies that are located in an internal bearing space that is formed between the outer ring and the inner ring, and that are arranged between the inner ring raceway and the outer ring raceway so as to be able to roll freely; and a seal ring that is formed into a circular ring shape and comprises: a fastening portion that is provided around an outer-circumferential edge portion, and that is fastened to one end portion of the outer ring; and a seal lip that is made of an elastic material, that is provided around an inner-circumferential edge portion, a tip-end edge of which comes in sliding contact with one end surface of the inner ring; the seal ring separating the internal bearing space and an external space; the seal lip comprising a plate-shaped connecting portion that is formed in a portion near a center in a radial direction than the tip-end edge; and a thick portion that is continuous from the connecting portion and having a thickness dimension that is greater than the connecting portion; and the tip-end edge being composed of an end edge in an axial direction of the thick portion; the fastening portion is fastened to a fastening groove that is formed in the inner-circumferential surface of the one end portion of the outer ring, the tip-end edge of the seal lip comes in sliding contact with the one end surface of the inner ring, and the one end surface of the inner ring is located at a position that is further recessed in the axial direction than the one end surface of the outer ring; characterized in that the rolling bearing with seal ring further comprises a second seal ring that is formed into a circular ring shape, that has: a second fastening portion provided around the outer-circumferential edge portion of the seal ring, and fastened to a fastening groove that is formed around the inner-circumferential surface of the other end portion of the outer ring; and a second seal lip made of an elastic material, provided around the inner-circumferential edge portion of the seal ring, a tip-end edge of which comes in sliding contact with part of the inner ring; the second seal ring separating the internal bearing space from external space; and by making the diameters of the second fastening portion and the second fastening groove of the second seal ring different from the diameters of the fastening portion and the fastening groove of the seal ring, error in assembling the seal ring and the second seal ring is prevented. an outer ring that is provided with an outer ring raceway around an inner-circumferential surface thereof; an inner ring that is provided with an inner ring raceway around an outer-circumferential surface thereof, and that is located on-an inner-diameter side of the outer ring so as to be concentric with the outer ring; a plurality of rolling bodies that are located in an internal bearing space that is formed between the outer ring and the inner ring, and that are arranged between the inner ring raceway and the outer ring raceway so as to be able to roll freely; and a seal ring that is formed into a circular ring shape and comprises: a fastening portion that is provided around an outer-circumferential edge portion, and that is fastened to one end portion of the outer ring; and a seal lip that is made of an elastic material, that is provided around an inner-circumferential edge portion, a tip-end edge of which comes in sliding contact with one end surface of the inner ring; the seal ring separating the internal bearing space and an external space; the seal lip comprising a plate-shaped connecting portion that is formed in a portion near a center in a radial direction than the tip-end edge; and a thick portion that is continuous from the connecting portion and having a thickness dimension that is greater than the connecting portion; and the tip-end edge being composed of an end edge in an axial direction of the thick portion; the fastening portion is fastened to a fastening groove that is formed in the inner-circumferential surface of the one end portion of the outer ring, the tip-end edge of the seal lip comes in sliding contact with the one end surface of the inner ring, and the one end surface of the inner ring is located at a position that is further recessed in the axial direction than the one end surface of the outer ring; characterized in that the rolling bearing with seal ring further comprises a second seal ring that is formed into a circular ring shape, that has: a second fastening portion provided around the outer-circumferential edge portion of the seal ring, and fastened to a fastening groove that is formed around the inner-circumferential surface of the other end portion of the outer ring; and a second seal lip made of an elastic material, provided around the inner-circumferential edge portion of the seal ring, a tip-end edge of which comes in sliding contact with part of the inner ring; the second seal ring separating the internal bearing space from external space; and by making the diameters of the second fastening portion and the second fastening groove of the second seal ring different from the diameters of the fastening portion and the fastening groove of the seal ring, error in assembling the seal ring and the second seal ring is prevented.