Current sensor is commonly used in a permanent magnet synchronous motor (PMSM) drive system. Occurrence of unexpected current sensor faults may cause feedback currents deviation and system degradation, which can be extremely detrimental to the safety of the industrial system with PMSM. This paper presents an estimation and rejection strategy of current sensor faults for a PMSM drive system. Sensor faults in current measurement circuits are treated as system disturbances by constructing a new system plant. A sliding mode observer and an improved equivalent-input-disturbance (EID) estimator are designed for the plant based on the EID theory. Accurate estimates of the current sensor equivalent-input-faults are thus obtained readily. Faults rejection is performed by subtracting the equivalent-input-faults from the control input. This allows an existing controller in a PMSM system to continue to function normally even a current sensor fault occurs. An existence analysis and stability proof are also discussed in detail for the system. Finally, different faults examples and a hardware-in-the-loop experiment are given to demonstrate the efficiency of the method.