Taylor one or two class number expansion is a common method for NURBS curve interpolation iteration, this method will cause the chord error and speed fluctuation. The difficulty of speed control in NURBS curve interpolation is due to the no exact analytical relationship between the curve and the parameter u. In order to complete the speed planning, it needs to be based on the speed control. Based on the two order Taylor expansion method, an improved method was proposed to obtain accurately interpolate point parameters by defining the search area and using the minimum deviation method based on the second order expansion method, so as to achieve precise speed control and provide speed control basis for acceleration and deceleration control. The experimental results show that the mean square error of the improved speed error is reduced by half, and the error precision of speed control is improved by an order of magnitude.