Organic-inorganic halide perovskite materials have emerged as attractive alternatives to conventional solar cell building blocks. Their high light absorption coefficients and long diffusion lengths suggest high power conversion efficiencies, and indeed perovskite-based single bandgap and tandem solar cell designs have yielded impressive performances. One approach to further enhance solar spectrum utilization is the graded bandgap, but this has not been previously achieved for perovskites. In this study, we demonstrate graded bandgap perovskite solar cells with steady-state conversion efficiencies averaging 18.4%, with a best of 21.7%, all without reflective coatings. An analysis of the experimental data yields high fill factors of ∼75% and high short-circuit current densities up to 42.1 mA cm-2. The cells are based on an architecture of two perovskite layers (CH3NH3SnI3 and CH3NH3PbI3-xBrx), incorporating GaN, monolayer hexagonal boron nitride, and graphene aerogel.