A robust data-aided (DA) signal-to-noise ratio (SNR) estimation algorithm in the time domain is proposed in this paper, aiming at the volatile Doppler shift and carrier wave phase offset under dynamical scenarios for M-ary phase shift keying (MPSK) over the flat-fading complex channel. The proposed algorithm exploits data aided, delay conjugate multiplies the received signal, converts Doppler shift into fixed phase factors, and overcomes the impacts of Doppler shift and carrier wave phase offset. Furthermore, the impact of noise is analyzed and simulation results show that, compared with algorithms based on the spectrum analysis (FFT), the proposed algorithm is superior in the performance, especially in the estimation accuracy under low SNR scenarios and has low complexity.