Abstract: Pulse compression is usually achieved using a matched filter to obtain the best output signal-to-noise ratio (SNR). However, for commonly used radar waveforms, the output of matched filters has high range sidelobes, which can easily result in target masking effect. It is often desirable to accept a slight penalty in the SNR to suppress range sidelobes using an optimized mismatched filter (MMF). Moreover, MMFs should be designed based on the radar waveforms with system distortion, which needs to be periodically obtained from real radar systems. Hence, MMF algorithms should be efficient. However, complex calculations, such as matrix inversion, are usually needed in existing algorithms, the large amount of computation of which is not suitable for hardware implementation. In this paper, a fast algorithm for MMF design based on dynamic alternating projection is proposed, and range sidelobes can be effectively suppressed under peak sidelobe level (PSL), integrated sidelobe level (ISL) and weighted ISL (WISL) criteria with constrained loss of SNR and mainlobe broadening. The proposed algorithm can be applied to different types of radar waveforms. Moreover, only simple calculations and fast Fourier transform (FFT) are used in the proposed algorithm, which is very suitable for hardware implementation.