PrV2Al20 is the heavy fermion superconductor based on the cubic Gamma3 doublet that exhibits non- magnetic quadrupolar ordering below ~ 0.6 K. Our magnetotransport study on PrV2Al20 reveals field-induced quadrupolar quantum criticality at Hc ~ 11 T applied along the [111] direction. Near the critical field Hc required to suppress the quadrupolar state, we find a marked enhancement of the resistivity rho(H, T), a divergent effective mass of quasiparticles and concomitant non-Fermi liquid (NFL) behavior (i.e. rho(T) ~ T^n with n < 0.5). We also observe the Shubnikov de Haas-effect above ?Hc, indicating the enhanced effective mass m/m0 ~ 10. This reveals the competition between the nonmagnetic Kondo effect and the intersite quadrupolar coupling, leading to the pronounced NFL behavior in an extensive region of T and H emerging from the quantum critical point.