Computer simulations of steady shear flow of nematic phases are performed using a nonequilibrium molecular dynamics. The SLLOD-type algorithm is applied to tie shear flows of Gay-Berne fluids which are nematic in the equilibrium states. Two Gay-Berne potentials with mu = 1, nu = 2 and mu = 2, nu = 1 are used and both molecular aspect ratios are set equal to 3. In the initial stage of shearing various patterns of the transient behavior are found in the order parameter and orientation angle, according to the initial conditions and shear rare. In the steady state the director is inclined to the flow at a constant angle regardless of the shear rate and the system becomes more highly oriented state. The fluids exhibit shear-thinning in viscosity and non-zero first and second normal stress differences.