Acceleration signal plays an important role in motion control systems. One of the main ways to obtain the acceleration is to calculate or estimate it from measured velocity. It deduced a mathematical model describing the relationship among velocity increments, true acceleration and noises based on the relationship between the signal and noise in the measurement speed. Regarding the true acceleration as an unknown parameter of the model, it proposed to estimate the acceleration by using the extended recursive least square method. Finally, it verified the effectiveness of the acceleration estimation method by simulation.