Linear frequency modulated (LFM) signal is widely used in wideband radars, where stretch processing is commonly adopted to reduce the processing bandwidth. In this paper, we propose a fast acceleration and velocity estimation method for wideband stretching LFM radars based on mutual bias correction. In this method, cross-correlation is carried out on adjacent stretched echoes to integrate scattering energy. By deriving the relationship between the two-dimensional (2D) spectrum of the cross-correlation result and the motion parameters, it is found that the frequency of the 2D spectrum peak is determined by the acceleration and the velocity. We first estimate a coarse acceleration using the frequency of the 2D spectrum peak on the slow time, and then construct a compensation function to estimate the coarse velocity. To obtain high precision estimation, we develop a mutual bias correction (MBC) process to reduce the bias of the coarse estimates. Experimental results show that the proposed method achieves much smaller root mean square error (RMSE) with comparable computational cost, compared to existing state-of-the-art methods.