The dechirp-receiving radar measures range by the frequency difference between the target echo and the reference signal. It can operate at a low sampling frequency while transmitting a wideband signal, which simplifies the radar hardware. However, when detecting high-speed and highly maneuvering targets, residual video phase (RVP), frequency mismatch, frequency modulation (FM) rate mismatch, and across range-Doppler unit (ARDU) problems occur after dechirp receiving, which cause difficulties in integrating the target echo and result in severe performance loss. To solve these problems, the dechirp generalized Radon-Fourier transform (DGRFT) and an algorithm for its fast implementation are proposed. The DGRFT compensates for the frequency and FM rate mismatch in the fast-time domain and the RVP in the fast-time frequency domain, and then implements joint envelope and phase compensations to overcome the ARDU phenomenon. After these compensations, the target echo can be effectively integrated. Experiments with simulated and measured data show that the performance of the DGRFT is better than that of the conventional moving target detector.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.