Abstract: A self-consistent Monte Carlo simulation method that includes charge exchange and elastic scattering is developed to calculate the energy and angle distributions of ions in cathode sheath of a DC argon gas discharge for the different pressures. Cross sections of the charge exchange and the momentum transfer that depend on the ion energy are taken into account precisely. It is found that, as the ions move towards the cathode, the high energy portions of ion energy distributions are enhanced gradually and the small-angle portions of the angle distributions increase. A strong field accelerates the ions to higher speed and ensures that more ions move along the lines of force. The self-consistent electric field spatial variation in the sheath is nonlinear.