A highly enantioselective [2+2] cycloaddition reaction of alkylidene malonates with the internal C[double bond, length as m-dash]C bond of N-allenamides was developed with a MgII/N,N'-dioxide complex as a catalyst. Various polysubstituted methylenecyclobutanes were afforded in good yields (up to 99%) and excellent enantioselectivities (up to 96% ee) under mild conditions. The utility of the donor-acceptor cyclobutane product was demonstrated as a masked 1,4-dipole in the formal [4+2] annulation reaction with a silyl enol ether.