The vector control method of current source inverter (CSI) driving permanent magnet synchronous motor (PMSM) requires the use of a dual closed-loop control with proportional-integral (PI) regulation for both current and voltage. However, the measurement errors of current and voltage sensors in this method can result in torque and speed ripples in the motor including one and twice the stator electrical frequency, which is inevitable. To address the aforementioned issue, this paper improves the adaptive selected harmonic elimination (ASHE) algorithm specifically targeting at the measurement errors in currents and voltages, thus compensating for the dq-axis currents and voltages. This approach eliminates the need for additional sensors and complex computations, swiftly eliminating error disturbances. Finally, the simulation results demonstrate the method’s efficacy in mitigating the negative impacts of measurement errors, significantly reducing speed and torque ripples.