Hybrid organic inorganic halide perovskites with the prototype material of CH3NH3PbI3 have recently attracted intense interest as low-cost and high-performance photovoltaic absorbers. Despite the high power conversion efficiency exceeding 20% achieved by their solar cells, two key issues-the poor device stabilities associated with their intrinsic material instability and the toxicity due to water-soluble Pb2+-need to be resolved before large-scale commercialization. Here, we address these issues by exploiting the 6 strategy of cation-transmutation to design stable inorganic Pb-free halide perovskites for solar cells. The idea is to convert two divalent Pb2+ ions into one monovalent M+ and one trivalent M3+ ions, forming a rich class of quaternary halides in double-perovskite structure. We find through first-principles calculations this class of materials have good phase stability against decomposition and wide range tunable optoelectronic properties. With photovoltaic-functionality-directed materials screening, we identify 11 optimal materials with intrinsic thermodynamic stability, suitable band gaps, small carrier effective masses, and low excitons binding energies as promising candidates to replace Pb-based photovoltaic absorbers in perovskite solar cells. The chemical trends of phase stabilities and electronic properties are also established for this class of materials, offering useful guidance for the development of perovskite solar cells fabricated with them.