Slotting at the base of spin-stabilized projectile is widely used in spinning rate measurement. Confined by the structure of the base, it only suits few models of projectile. For the projectiles with special structures, such as apertures or holes at the base, the information of spinning rate in radar echo is considerably so weak that the conventional signal processing methods become invalid. Herein, a method based on acceleration compensation is proposed to extract the spinning rate from the echo of low signal to noise rate (SNR). First, an algorithm called Two Segments based FFT is adopted to estimate the coarse rate of linear frequency modulation (LFM). Next, using the coarse rate as the initial value of optimization, Golden Section method is used to search the fine rate of LFM to improve the accuracy of estimation. Then, the fine value is used to construct the reference LFM signal and compensate the effect of acceleration. At last, based on Chirp Z Transform, the method of spectrum zooming is employed to alleviate the spectrum leakage and improve the performance of spinning rate processing. Simulation shows that the precision of the spinning rate measurement is better than 0.25% for majority of the modulation indices when the SNR equals
to 0 dB.