Based on the nonlinear system theory， the stability and convergence of adaptive filtering measurement for power signals are analyzed and demonstrated to find its convergent condition and to design an appropriate adaptive filtering measurement method. Traditional steady measurement is an open-loop method and may misjudge in case of asynchronous sample and signal disturbances. The adaptive filtering measurement method is a close-loop method and it can be employed to deal with non-sin and non-period data， caused by asynchronous sample and non-integer harmonics， and to estimate and correct distortion. The adaptive filtering measurement method can be applied in accurate and reliable measurement in the steady power system.