We investigate the pressure effects on the electronic structures and phonon properties of rare-earth-based cubic-Heusler compound LuPd_{2}In, on the basis of ab initio density functional theory. We find the occurrence of intriguing phase transition from the superconducting (SC) to charge-density wave (CDW) state under pressure (P), which is quite unusual in that the pressure is detrimental to the CDW state in usual systems. The SC transition temperature T_{C} of LuPd_{2}In increases first with increasing pressure, up to P_{C}≈28 GPa, above which a quantum phase transition into the CDW state takes place. This extraordinary transition originates from the occurrence of phonon softening instability at a special q=M in the Brillouin zone. We thus propose that LuPd_{2}In is a quite unique material, in which the CDW quantum critical point is realized under the SC dome by applying the pressure.