Twenty-micrometer-thick single-crystal methylammonium lead triiodide (MAPbI3) perovskite (as an absorber layer) grown on a charge-selective contact using a solution space-limited inverse-temperature crystal growth method yields solar cells with power conversion efficiencies reaching 21.09% and fill factors of up to 84.3%. These devices set a new record for perovskite single-crystal solar cells and open an avenue for achieving high fill factors in perovskite solar cells.