The emergence of halide double perovskites significantly increases the compositional space for lead-free and air-stable photovoltaic absorbers compared to halide perovskites. Nevertheless, most halide double perovskites exhibit oversized band gaps (>1.9 eV) or dipole-forbidden optical transition, which are unfavorable for efficient single-junction solar cell applications. The current device performance of halide double perovskite is still inferior to that of lead-based halide perovskites, such as CH3NH3PbI3 (MAPbI3). Here, by ion type inversion and anion ordering on perovskite lattice sites, two new classes of pnictogen-based quaternary antiperovskites with the formula of X6B2AA' and X6BB'A2 are designed. Phase stability and tunable band gaps in these quaternary antiperovskites are demonstrated based on first-principles calculations. Further photovoltaic-functionality-directed screening of these materials leads to the discovery of 5 stable compounds (Ca6N2AsSb, Ca6N2PSb, Sr6N2AsSb, Sr6N2PSb, and Ca6NPSb2) with suitable direct band gaps, small carrier effective masses and low exciton binding energies, and dipole-allowed strong optical absorption, which are favorable properties for a photovoltaic absorber material. The calculated theoretical maximum solar cell efficiencies based on these five compounds are all larger than 29%, comparable to or even higher than that of the MAPbI3 based solar cell. Our work reveals the huge potential of quaternary antiperovskites in the optoelectronic field and provides a new strategy to design lead-free and air-stable perovskite-based photovoltaic absorber materials.