We calculated magnetic exchange constants and magnetocaloric properties of Ni2Mn1−xCuxGa Heusler alloys by ab initio and Monte Carlo methods. The ab initio study of the influence of the Cu excess x on the strength of magnetic interactions revealed that Cu weakens Mn-Ni interaction and has a complex impact on the Mn-Mn interactions. Theoretically calculated magnetic phase diagram of Ni2Mn1−xCuxGa is in a good agreement with available experimental data. Calculated by the Monte Carlo method the isothermal magnetic entropy change ΔSmag in a Ni2Mn0.75Cu0.25Ga alloy is significantly smaller around the coupled magnetostructural phase transition temperature than the reported earlier experimental ΔSmag. This discrepancy is ascribed to an overestimation of the experimental ΔSmag at the magnetostructural phase transition. Theoretically determined adiabatic temperature change ΔTad in Ni2Mn0.75Cu0.25Ga agrees well with ΔTad measured experimentally by a direct method.