Multi-piece golf balls having at least one layer made from a polyamide non-ionomeric composition are provided. The polyamide composition consists essentially of about 40 to about 99% by weight polyamide; about 1 to about 60% by weight of an acid anhydride-modified polyolefin; and about 1 to about 60% of a fatty acid additive selected from the group consisting of fatty acid salts, fatty acid amides, and mixtures thereof. The ball includes a core, preferably a dual core construction; and a cover of at least one layer. In another preferred construction, a multi-layered core containing an inner, intermediate, and outer core layer is made. For example, the intermediate core layer may be made of a rubber composition; and each of the inner core and outer core layers may be made of the polyamide composition. The resulting ball has high resiliency along with a soft feel.