When both inversion and time-reversal symmetries are broken, the critical current of a superconductor can be nonreciprocal. In this work we show that in certain classes of two-dimensional superconductors with antisymmetric spin-orbit coupling, Cooper pairs acquire a finite momentum upon the application of an in-plane magnetic field, and as a result, critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal. This supercurrent diode effect is also manifested in the polarity-dependence of in-plane critical fields induced by a supercurrent. These nonreciprocal effects may be found in polar SrTiO3 film, few-layer MoTe2 in the Td phase, and twisted bilayer graphene in which the valley degree of freedom plays the role analogous to spin.