The rubber composition for use in manufacturing a solid core of a multilayer-structured golf ball or a one-piece golf ball contains a co-curing agent and preferably an organic sulfur compound micro-encapsulated within a thermoplastic resin whose softening point is in a range of 80-250.degree. C. This improves dispersibility of the co-curing agent and the organic sulfur compound within the rubber composition, and enables adjustment of a crosslinking pattern of rubber molecule main chains, so that rebound performance of the golf ball is improved.