We study the structural, electronic, and magnetic properties of the SrCrO3/YCrO3 superlattice and their dependence on epitaxial strain. We discover that the superlattice adopts A-type antiferromagnetic (A-AFM) ordering in contrast to its constituents (SrCrO3: C-AFM; YCrO3: G-AFM) and retains it under compressive strain while becoming ferromagnetic (5 μB per formula unit) at +1% strain. The obtained ferroelectric polarization is significantly higher than that of the R2NiMnO6/La2NiMnO6 (R = Ce to Er) series of superlattices [Nat. Commun. 5, 4021 (2014)] due to a large difference between the antipolar displacements of the Sr and Y cations. The superlattice is a hybrid-improper multiferroic material with a spontaneous ferroelectric polarization (13.5 μC/cm2) approaching that of bulk BaTiO3 (19 μC/cm2). The combination of ferromagnetism with ferroelectricity enables multistate memory applications. In addition, the charge-order-driven p-type semiconducting state of the ferromagnetic phase (despite the metallic nature of SrCrO3) is a rare property and interesting for spintronics. Monte Carlo simulations demonstrate a magnetic critical temperature of 90 K for the A-AFM phase without strain and of 115 K for the ferromagnetic phase at +5% strain, for example.