Multi-piece golf balls having a solid core and cover are provided. The ball contains an inner core made of a foam composition and surrounding outer core layer. Preferably, foamed polyurethane is used to form the inner core and polybutadiene rubber is used to make the outer core. The specific gravity (density) of the inner core is preferably less than the density of the outer core. The outer surface of the inner core preferably has a non-uniform structure and includes projecting members. The ball preferably has a high Moment of Inertia (MOI). The ball includes a single or multi-layered cover surrounding the core structure.