The acceleration of a high maneuvering target in signal processing is helpful to enhance the performance of the tracker and facilitate the classification of targets. At present, most of the research on acceleration estimation is carried out in cases of a single target with time-frequency analysis methods such as fractional Fourier transform(FRFT), Hough-ambiguity transform(HAT), and Wigner-Ville distribution(WVD), which need to satisfy enough time duration and sampling theorem. Only one reference proposed a method of acceleration estimation for multiple targets based on modified polynomial phase transform(MPPT) in the linear frequency modulation(LFM) continuous-wave(CW) radar. The method of acceleration estimation for multiple targets in the pulse Doppler(PD) radar has not been reported so far. Compressive sensing(CS) has the advantage of sampling at a low rate and short duration without sacrificing estimation performance. Therefore, this paper proposes a new method of acceleration estimation for multiple maneuvering targets with the unknown number based on CS with pulse Doppler signals. Simulation results validate the effectiveness of the proposed method under several conditions with different duration, measurement numbers, signal to noise ratios(SNR), and regularization parameters, respectively. Simulation results also show that the performance of the proposed method is superior to that of FRFT and HAT in the condition of multiple targets. The acceleration of a high maneuvering target in signal processing is helpful to enhance the performance of the tracker and facilitate the classification of targets. At present, most of the research on acceleration estimation is carried out in cases of a single target with time-frequency analysis Methods such as fractional Fourier transform (FRFT), Hough-ambiguity transform (HAT), and Wigner-Ville distribution (WVD), which need to satisfy enough time duration and sampling theorem. Only one reference proposed a method of acceleration estimation for multiple targets based on modified polynomial phase transform (MPPT) in the linear frequency modulation (LFM) continuous-wave (CW) radar. The method of acceleration estimation for multiple targets in the pulse Doppler (PD) radar has not been reported so far. (CS) has the advantage of sampling at a low rate and short duration without sacrificing estimation performance. Therefore, this paper proposes a new method of acceleration est imation for multiple maneuvering targets with the unknown number based on CS with pulse Doppler signals. Simulation results also show that the performance of the proposed method is superior to that of FRFT and HAT in the condition of multiple targets.