The influence of Cu doping on phase transition, thermal strain, and thermal expansion property of polycrystalline Ni50Mn23 -xCuxGa27( x = 1, 3, 5, 6 and 7) alloys is investigated. The results show that with increasing Cu concentration, martensitic transformation gradually gets close to Curie transition. A magnetostructural transition (MST) is observed in samples with x = 6 and 7. Such MST can enhance magnitude of transformation strain. Besides, Ni50Mn23 xCuxGa27 alloys possess an isotropic, recoverable, and thermally stable thermal strain. Excitedly, Cu doping can effectively tune the phase transition, thermal strain, and thermal expansion properties of Ni(50)Mn(23-x)CuxGa(27) alloys. Adjustable coefficients of thermal expansion from positive to negative are obtained by Cu-doped Ni(50)Mn(23-x)CuxGa(27) alloys. The average linear expansion coefficient (alpha) between -140.44 and -207.70 ppm K-1 is observed in salmples with x = 6 and 7 for a narrow temperature span of 11-14 K. When the temperature span is about 72 K ( x = 6) and 73 K ( x = 7), which is the largest temperature span observed in Ni-Mn-Ga-based alloys recently, the a values decrease to about 36 ppm K-1. These findings are beneficial for manipulating the thermal expansion property of Ni-Mn-Ga-Cu alloys and their multifunctional applications.