Multi-piece golf balls having a solid core and cover are provided. The ball contains a small, heavy inner core and surrounding outer core layer. The inner core preferably contains metal materials such as copper, steel, brass, tungsten, titanium, nickel, iron, tin, and bronze particles dispersed in a thermoset or thermoplastic polymeric matrix. Preferably, the polymeric matrix comprises polybutadiene rubber. The outer surface of the inner core preferably has a non-uniform structure and includes projecting members. For example, the outer surface may contain multiple projecting ribs with gaps located between the ribs. The ball includes a cover surrounding the core structure. The cover may be multi-layered.