The Monte Carlo method is applied to study the nonequilibrium steady-state structure and non-Newtonian viscosity of a sheared simple liquid, The simulation is performed in-plane Couette flow geometry on the basis of the nonequilibrium statistical mechanical formalism provided by the nonequilibrium ensemble method. The results are compared with those by the nonequilibrium molecular-dynamics simulation results and also those by the integral equation method. The present Monte Carlo method is comparable in accuracy with the molecular-dynamics simulation method for the quantities compared.