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We have studied the magneto-transport properties of a series of ZrNi2-xCuxGa compounds. For all Cu concentration (x ≤ 0.5) the samples exhibited the L21 cubic structure at room temperature and demonstrated superconductivity below 2 K. A superconducting phase transition temperature of as low as ∼1 K and a critical magnetic field of 1.78 T was observed in the system. A linear extrapolation of TC to T = 0 highly indicated that a stoichiometry-dependent superconducting quantum phase transition may occur in ZrNi2-xCuxGa at xc = 0.90.