In this study, the evolution of the velocity field and scalar concentration fields in stably stratified shear flow is studied using direct numerical simulations. Two cases with vertical mean shear and horizontal mean shear are compared. In both cases, the growth of the turbulent kinetic energy weakens as the Richardson number is increased. However, the horizontal shear case shows a stronger growth of the turbulent kinetic energy than the vertical shear case for a given Richardson number. The ordering of the velocity components was found to change from streamwise > horizontal > vertical in the vertical shear case to streamwise > vertical > horizontal in the horizontal shear case. The fluctuation level of a passive species variable with a vertical mean gradient was observed to be stronger in the horizontal shear case. The ratio of the vertical turbulent eddy diffusivity to the horizontal turbulent eddy diffusivity was found to be larger in the horizontal shear case.