Double perovskites in the form of A₂B′B′′X₆ (A = Cs, B′ = Ag, B′′ = Bi) have been reported as potential alternatives to lead-containing organometal trihalide perovskites. However, all double perovskites synthesized to date exhibit indirect bandgaps >1.95 eV, which are undesirable for photovoltaic and optoelectronic applications. Herein, we report a comprehensive computer-aided screening of In- and Ga-based double perovskites for potential photovoltaic applications. To this end, several preconditions are implemented for the screening of optimal candidates, which include structural stability, electronic bandgaps, and optical absorption. Importantly, four In- and Ga-based double perovskites are identified to possess direct bandgaps within the desirable range of 0.9–1.6 eV for photovoltaic applications. Dominant optical absorption of the four double perovskites is found to be in the UV range. The structural and thermal stability of the four double perovskites are examined using both the empirical Goldschmidt ratio and convex-hull calculations. Only Cs₂AgInBr₆ is predicted to be thermodynamically stable.