The classic measurement-based method for load model parameter identification relies on lots of transient simulations and optimization iterations, which is computationally intensive, and is unsuitable to the terminal devices for recording load characteristic to participate in grid edge computing. To solve this difficulty, a fast identification method for load model parameters based on jumping and steady-state points of measured data is proposed, which greatly reduces the calculation time by avoiding the transient simulations and random optimizations of the classic method, and at the same time, well retains the accuracy of identified parameters. Firstly, the method extracts four points of measured data as calculation points, i.e., the point after voltage sag, two points before and after voltage recovery, and the final steady-state point. Then, the method calculates the state variables and powers at the four points through steady-state calculation, implicit trapezoid integration method and Hermite-Simpson method respectively. Finally, according to the measured powers of the four points, the method provides an initial key load model parameters through polynomial approximation method and finds the optimal parameters through Nelder-Mead algorithm. The accuracy and practicality of the method are demonstrated by test and field case studies, and the computation burden is less than 2.5% of that in the classic method without obvious loss of identification accuracy.INDEX TERMS load model parameter identification, jumping and steady-state point, Hermite-Simpson method, polynomial approximation, Nelder-Mead algorithm.