A golf ball having a cover composed of a polyurethane formed from a p-phenylene diisocyanate (PPDI) based polyurethane prepolymer is disclosed herein. The PPDI-based polyurethane prepolymer is formed from a PPDI and a polyol such as polycaprolactone. The PPDI-based polyurethane prepolymer is cured with a curative such as a 1,4 butane diol and glycol. The PPDI-based polyurethane cover may be either thermoset or thermoplastic. The PPDI-based polyurethane cover has a high flexural modulus at a lower hardness which gives a better feel yet maintains good distance, higher Bashore resilience, higher tensile strength, higher tear resistance, improved elongation, and better playability and control. These benefits and improvements are exhibited even though the cover of the present invention is thinner than those of conventional golf balls. The present invention also provides new golf balls having durable thin covers thereby enabling golf balls with large cores. It is well understood that increasing the core diameter of a golf ball generally translates into an increased COR which in turn generally translates into an increased initial velocity and enhanced overall travel distance.