In order to address an all-inorganic halide lead-free perovskite for potential photovoltaic applications, we carried out first-principles calculations of bandgaps of 260 all-inorganic halide perovskites belonging to the class ABX3, with A = Li, Na, K, Rb, Cs, B = Pb, Sn, and Ge, and X = F, Cl, Br, I. Three most common crystal symmetries were chosen, including cubic, tetragonal, and two orthorhombic phases. The bandgap exhibited increase with the decreasing of the anions radius (I, Br, Cl, F) and lowering the symmetry of the structures. With consideration of multiple factors forming perovskites, we reported three all-inorganic lead-free halides perovskites including cubic-KSnCl3, cubic-RbSnCl3, and trigonal-NaGeBr3 as candidates with desirable bandgap (1.24–1.44 eV) for photovoltaic applications.