A centrifugal pump operates under off-design operation conditions would lead to flow instability, additional energy loss or mechanical damage. Early detection is of great importance to its operation efficiency and safety. Sensorless monitoring technology based on motor current signature analysis (MCSA) is a cost-effective and non-intrusive technology to monitor motor-driven devices. However, existing researches on MCSA for centrifugal pump usually realize their monitoring function through complicated time-frequency or energy analysis, they stop short of an indicator that has less calculation cost and definite physical significance compatible with the pump’s operation condition. In response to the limitations, this paper aimed at establishing such indicator for centrifugal pump based on MCSA. Theoretical analysis, CFD simulation and experiments were conducted to study the characteristics of pump torque and motor stator current, whose results suggest that the torque fluctuation frequency characteristics would be transmitted to motor stator current by electromagnetic coupling effect, and distribute as sidebands in current spectrum through power frequency modulation. As a result, torque disturbance caused by off-design operation would be reflected as stronger harmonic and noise distortion of motor stator current, and the distortion intensity could be quantified and employed as the operation condition indicator (OCI) for centrifugal pump. Experimental results show that the OCI has its lowest value under the design operation condition, and gradually increases as the pump’s operation condition getting worse. Such change law agrees well with the efficiency characteristics of centrifugal pump, which provides a new thought for the operation monitoring of centrifugal pump based on MCSA. The proposed indicator could be directly obtained from the current signal and easily calculated, which is more appropriate for application and probably more preferred for industry compared to the former operation monitoring methods.