This paper proposes a current sensorless drive method by using the mathematical modeling of a surface-mounted permanent magnet synchronous motor (SPMSM) and a dead-time compensation method to reduce the calculated current error caused by differences between real output voltages and voltage commands. The proposed method is implemented by using only a processor algorithm internally, i.e., without any voltage-sensing circuit hardware, such as filtering circuits and current sensor feedback circuits. To show the effectiveness of the proposed method, MATLAB simulations are carried out with an Electric Power Steering (EPS) System containing an SPMSM, a motor drive system and a mechanical gear system. The result shows the validity of the proposed method.