We report the discovery of a pressure-induced heavy fermion superconductivity in a nonmagnetic orbital ordering state in the cubic compound PrTi(2)Al(20). In particular, we found that the transition temperature and the effective mass associated with the superconductivity are dramatically enhanced as the system approaches the putative quantum critical point of the orbital order. Our experiment indicates that the strong orbital fluctuations may provide a nonmagnetic glue for Cooper pairing.