A pulley apparatus, comprising: a rolling bearing having an inner ring that has an inner ring raceway around the outer circumferential surface thereof, an outer ring that has an outer ring raceway around the inner circumferential surface thereof, and a plurality of rolling elements that are provided between the inner ring raceway and the outer ring raceway; and a pulley that has an outer circumferential surface around which a belt is placed, and an inner circumferential surface that is fitted around the outer circumferential surface of the outer ring; wherein locking grooves (16b, 16c) are formed in two locations in the axial direction of the outer circumferential surface of the outer ring; grooves (16b, 16c) respectively having a width that is within the range of 1/20 to 1/2 the width of the outer ring; knurling (19b, 19c) is formed on the bottom surface of the locking grooves (16b, 16c) by a knurling process such that concave sections (17b, 17c) and convex sections (18b, 18c) that extend in the width direction in a state so as to incline at the same angle with respect to the axial direction in opposite directions from each other are alternately arranged around the entire circumference; each of these concave sections (17b, 17c) comprising a bottom surface and two inside surfaces on both sides in the circumferential direction of the bottom surface and that are continuous with the tip end surfaces of the adjacent convex sections (18b, 18c); these concave sections (17b, 17c) having a trapezoidal shape; and a plurality of trapezoidal shaped protrusions that extend in the width direction and in an inclined state with respect to the axial direction and that engage with the concave sections are formed around two locations in the axial direction of the inner circumferential surface of the pulley. a rolling bearing having an inner ring that has an inner ring raceway around the outer circumferential surface thereof, an outer ring that has an outer ring raceway around the inner circumferential surface thereof, and a plurality of rolling elements that are provided between the inner ring raceway and the outer ring raceway; and a pulley that has an outer circumferential surface around which a belt is placed, and an inner circumferential surface that is fitted around the outer circumferential surface of the outer ring; wherein locking grooves (16b, 16c) are formed in two locations in the axial direction of the outer circumferential surface of the outer ring; grooves (16b, 16c) respectively having a width that is within the range of 1/20 to 1/2 the width of the outer ring; knurling (19b, 19c) is formed on the bottom surface of the locking grooves (16b, 16c) by a knurling process such that concave sections (17b, 17c) and convex sections (18b, 18c) that extend in the width direction in a state so as to incline at the same angle with respect to the axial direction in opposite directions from each other are alternately arranged around the entire circumference; each of these concave sections (17b, 17c) comprising a bottom surface and two inside surfaces on both sides in the circumferential direction of the bottom surface and that are continuous with the tip end surfaces of the adjacent convex sections (18b, 18c); these concave sections (17b, 17c) having a trapezoidal shape; and a plurality of trapezoidal shaped protrusions that extend in the width direction and in an inclined state with respect to the axial direction and that engage with the concave sections are formed around two locations in the axial direction of the inner circumferential surface of the pulley.