Recently, inorganic copper-based halide perovskites and their derivatives (CHPs) with chemical formulas A_lCu_mX_n (A = Rb and Cs; X = Cl, Br and I; l, m, and n are integers.), have received increasing attention in the photoluminescence field, due to their lead-free, cost-effective, earth-abundant and low electronic dimensionality. Ascribed to flexible valence charge of Cu (Cu¹⁺ and Cu²⁺) and complex competing phases, the crystal structures and phase stabilities of CHPs are complicated and ambiguous, which limits their experimental applications. Via comprehensive first-principles calculations, we have investigated thermodynamic stabilities of possible crystal phases for A_lCu_mX_n by considering all the possible secondary phases existing in inorganic crystal structure database (ICSD). Our results are in agreement with existing experiments and further predicted the existence of 10 stable CHPs, i.e. Rb₃Cu₂Br₅, Rb₃Cu₂I₅, RbCu₂Cl₃, Rb₂CuI₃, Rb₂CuBr₄, RbCuBr₃, Rb₃Cu₂Br₇, Cs₃Cu₂Br₇, Cs₃Cu₂Cl₇ and Cs₄Cu₅Cl₉, which have not yet been reported in experiments. This work provides a phase and compositional map that may guide experiments to synthesize more novel inorganic CHPs with diverse properties for potential functional applications.