Abstract: The basic principle of B-spline least squares is firstly introduced in this paper. The computing method is given based on there order B-spline least squares. This method contains the characteristics of fitting,numerical differentiation,smoothing that can be used to calculate the acceleration from velocity. The GPS velocity data and simulation velocity data of airborne vector gravimetry is processed to yield the smoothed acceleration by using the computing method above. Then,the amplitude spectrum of the smoothed acceleration is calculated by a Fourier transform. The result from the amplitude spectrum indicates that the high frequency components in the raw GPS acceleration are smoothed out.