Abstract: Sampling may cause some loss for coherent integration in time domain and the computation burdens of the common coherent integration algorithms are usually heavy. To resolve these issues, a fast algorithm realizing long-term coherent integration in fast-time frequency domain is proposed. The algorithm firstly utilizes non-uniform FFT to accomplish range walk correction and phase compensation in fast-time frequency domain, and then fulfills the integration via IFFT. The proposed algorithm can avoid loss entailed by sampling, and needs relatively less computation. The theoretical analysis and simulation results demonstrate the effectiveness of the proposed algorithm.