Significant manifestation of interplay of superconductivity and charge density wave, spin density wave or magnetism is dome-like variation in superconducting critical temperature (Tc) for cuprate, iron-based and heavy Fermion superconductors. Overall behavior is that the ordered temperature is gradually suppressed and the Tc is enhanced under external control parameters. Many phenomena like pesudogap, quantum critical point and strange metal emerge in the different doping range. Exploring dome-shaped Tc in new superconductors is of importance to detect emergent effects. Here, we report that the observation of superconductivity in new layered Cu-based compound RE2Cu5As3O2 (RE=La, Pr, Nd), in which the Tc exhibits dome-like variation with maximum Tc of 2.5 K, 1.2 K and 1.0 K as substituting Cu by large amount of Ni ions. The transitions of T* in former two compounds can be suppressed by either Ni doping or rare earth replacement. Simultaneously, the structural parameters like As-As bond length and c/a ratio exhibit unusual variations as Ni-doping level goes through the optimal value. The robustness of superconductivity, up to 60% of Ni doping, reveals the unexpected impurity effect on inducing and enhancing superconductivity in this novel layered materials