A golf ball having windings of strands made of a highly neutralized acid polymer is disclosed. The presence of a high acid content may cause the highly neutralized acid polymer to exhibit certain material properties. For example, the high acid content may cause an increased hardness and an increased flexural modulus. A high hardness may result in a golf ball exhibiting increased distance off the tee, or increased COR, among other desirable play characteristics. The hardness of the golf ball corresponds with the feel of the golf ball. The construction of a golf ball including wound strands may provide a soft feel. Thus, providing windings of bands made from a highly neutralized acid polymer may provide a golf ball with an increased distance off the tee and a soft feel.