Males and females often differ in their fitness optima for shared traits that have a shared genetic basis, leading to sexual conflict. Morphologically differentiated sex chromosomes can resolve this conflict and protect sexually antagonistic variation, but they accumulate deleterious mutations. However, how sexual conflict is resolved in species that lack differentiated sex chromosomes is largely unknown. Here we present a chromosome-anchored genome assembly for rainbow trout (Oncorhynchus mykiss) and characterize a 55-Mb double-inversion supergene that mediates sex-specific migratory tendency through sex-dependent dominance reversal, an alternative mechanism for resolving sexual conflict. The double inversion contains key photosensory, circadian rhythm, adiposity and sex-related genes and displays a latitudinal frequency cline, indicating environmentally dependent selection. Our results show sex-dependent dominance reversal across a large autosomal supergene, a mechanism for sexual conflict resolution capable of protecting sexually antagonistic variation while avoiding the homozygous lethality and deleterious mutations associated with typical heteromorphic sex chromosomes.