Golf balls containing at least one layer made from a thermoset polyurethane or polyurethane-urea that is the reaction product of a polyisocyanate with moisture-resistant polyol and a curing agent are provided. The moisture-resistant polyol may be prepared by dimerizing unsaturated aliphatic monocarboxylic acid or ester containing 10 to 60 carbon atoms followed by reacting it with a monomeric, oligomeric, or polymeric diol. In one preferred version, the moisture-resistant polyol is a branched polyester polyol containing 36 carbon atoms. The composition can be prepared using prepolymer or one-shot manufacturing techniques. The thermoset composition has good cross-link density. The resulting golf ball has desirable playing performance properties including high resiliency, toughness, impact durability, moisture-resistance, and soft feel.