The present invention provides a multi-layer structure golf ball having a thread rubber layer, which has good shot feel and controllability as well as satisfactory flight performance and cut resistance. The golf ball includes a thread wound core and a cover covering the thread wound core, wherein the cover is formed from a heated mixture of: (A) an ionomer resin, (B) a thermoplastic elastomer having a carboxyl group or a thermoplastic elastomer having a terminal OH group, and (C) a block copolymer having a styrene-butadiene-styrene structure in which the polybutadiene block contains epoxy groups, or a block copolymer having styrene-isoprene-styrene structure in which the polyisoprene block contains epoxy groups, the cover has a flexural modulus of from 50 to 300 MPa and a Shore D-scale hardness of from 40 to 60.