Orbital degrees of freedom in condensed matters could play important roles in forming a variety of exotic electronic states by interacting with conduction electrons. In 4f electron systems, because of strong intra-atomic spin-orbit coupling, an orbitally degenerate state inherently carries quadrupolar degrees of freedom. The present work has focussed on a purely quadrupole-active system PrIr2Zn20 showing superconductivity in the presence of an antiferroquadrupole order at TQ = 0.11 K. We observed non-Fermi liquid (NFL) behaviors emerging in the electrical resistivity and the 4f contribution to the specific heat, C_4f, in the paramagnetic state at T > TQ. Moreover, in magnetic fields below 6 T, all data set of the electrical resistivity and C_4f(T) are well scaled with characteristic temperatures T0s. This is the first observation of the NFL state in the nonmagnetic quadrupole-active system, whose origin is intrinsically different from that observed in the vicinity of the conventional quantum critical point. It implies possible formation of a quadrupole Kondo lattice resulting from hybridization between the quadrupoles and the conduction electrons. Below 0.13 K, the electrical resistivity and C_4f(T) exhibit anomalies as B approaches 5 T. This is the manifestation of a field-induced crossover toward a Fermi-liquid ground state in the quadrupole Kondo lattice.