A sealing structure comprising: a torsional vibration damper having a tubular part to be attached to a crankshaft; and an oil seal configured to seal an annular gap between an inner circumferential surface of a shaft hole in a housing for the crankshaft to pass through and an outer circumferential surface of the tubular part, the oil seal including a reinforcing ring having a cylindrical part, and an inward flange part provided at an end on an opposite side from a sealed-fluid side of the cylindrical part, and a sealing body made of an elastic material and provided integrally with the reinforcing ring, the reinforcing ring being configured such that a portion on an end face of the inward flange part on the opposite side from the sealed-fluid side is exposed, the sealing body including: an oil lip extending from near a distal end of the inward flange part toward the sealed-fluid side and slidable on the outer circumferential surface of the tubular part; and a dust lip extending from near the distal end of the inward flange part toward the opposite side from the sealed-fluid side and slidable on the outer circumferential surface of the tubular part; characterized by a side lip extending from near the distal end of the inward flange part radially inward and further toward the opposite side from the sealed-fluid side than the dust lip to a position not as far as the outer circumferential surface of the tubular part, an annular member fixed to the outer circumferential surface of the tubular part further on the opposite side from the sealed-fluid side than the side lip and covering an outer circumferential surface of the side lip such that there is a gap between the annular member itself and the outer circumferential surface of the side lip. a torsional vibration damper having a tubular part to be attached to a crankshaft; and an oil seal configured to seal an annular gap between an inner circumferential surface of a shaft hole in a housing for the crankshaft to pass through and an outer circumferential surface of the tubular part, the oil seal including a reinforcing ring having a cylindrical part, and an inward flange part provided at an end on an opposite side from a sealed-fluid side of the cylindrical part, and a sealing body made of an elastic material and provided integrally with the reinforcing ring, the reinforcing ring being configured such that a portion on an end face of the inward flange part on the opposite side from the sealed-fluid side is exposed, the sealing body including: an oil lip extending from near a distal end of the inward flange part toward the sealed-fluid side and slidable on the outer circumferential surface of the tubular part; and a dust lip extending from near the distal end of the inward flange part toward the opposite side from the sealed-fluid side and slidable on the outer circumferential surface of the tubular part; an oil lip extending from near a distal end of the inward flange part toward the sealed-fluid side and slidable on the outer circumferential surface of the tubular part; and a dust lip extending from near the distal end of the inward flange part toward the opposite side from the sealed-fluid side and slidable on the outer circumferential surface of the tubular part; characterized by a side lip extending from near the distal end of the inward flange part radially inward and further toward the opposite side from the sealed-fluid side than the dust lip to a position not as far as the outer circumferential surface of the tubular part, a side lip extending from near the distal end of the inward flange part radially inward and further toward the opposite side from the sealed-fluid side than the dust lip to a position not as far as the outer circumferential surface of the tubular part, an annular member fixed to the outer circumferential surface of the tubular part further on the opposite side from the sealed-fluid side than the side lip and covering an outer circumferential surface of the side lip such that there is a gap between the annular member itself and the outer circumferential surface of the side lip.