In oceanographic situations where salt fingers may be an important mechanism for the transport of heat and salt in the vertical, velocity shears may also be present. Salt finger convection is analogous to Bénard convection in that the kinetic energy of the motions is obtained from the potential energy stored in the unstable distribution of a stratifying component. On the basis of the thermal analogy it is of interest to discover whether salt fingers are converted into two-dimensional sheets by the wind shear, and how the vertical fluxes of heat and salt are changed by the wind shear. Salt finger convection under the effect of steady wind shear is theoretically examined in this paper. The evolution of instability developing in the presence of a vertical density gradient disturbance and the horizontal Couette flow is considered near the onset of salt fingers under a moderate rate of shear. We use velocity as the basic variable and solve the pressure Poisson equation in terms of the associated Green function. Growth competition between the longitudinal rolls (LR) and the transverse rolls (TR), whose axes are respectively in the direction parallel to and perpendicular to the Couette flow, is investigated by the weakly nonlinear analysis of coupled-mode equations. The results show that the TR mode is characterized in some range of the effective Rayleigh number, and that the stability is dominated by the LR mode in the system.