Effects of wind on quasi-steady, shallow convection in the Martian boundary layer are studied using a large-eddy simulation model. Convection in the model is generated by the radiative flux divergence and the strength of the surface heat flux, which do not vary in time. The resulting convective boundary layer exhibits transient, irregular, horizontal cellular structures, transported by wind, and a lack of well-pronounced regular horizontal rolls, observed for analogous conditions on Earth. The dimensionless statistics of turbulence are generally similar to those generated in the windless conditions, and depend on the ratio F, defined in terms of the integrated radiative and turbulent heating rates in the boundary layer. The simulations show that variations of the radiative heating influence the temperature statistics, while their effects on the wind velocity are relatively small. The horizontal velocity variances do not show a strong dependence on parameter F, in contrast with the vertical velocity variances, which are strongly dependent on F.