MDPS (motor driven power steering) systems have been widely used in vehicles due to their improved fuel efficiency and steering performance when compared to conventional hydraulic steering. However, the reduction of torque ripples and material cost are important issues. A low resolution position sensor for MDPS is one of the candidates for reducing the material costs. However, it may increases the torque ripple due to the current harmonics caused by low resolution encoder signals. In this paper, the torque ripple caused by the quantized rotor position of the low resolution encoder is analyzed. To reduce the torque ripples caused by the quantization of the encoder signals, the rotor position and the speed are estimated by measuring the frequency of the encoder signals. In addition, the compensating q-axis current is added to the current command so that the 6th order torque harmonic is attenuated. The reduction of torque ripples by applying the estimated rotor position and the compensated q-axis current is verified through experimental results.