Abstract: Blind demodulation of constellation modulated signals such as Multiple Phase Shift Keying (MPSK) and Multiple Quadrature Amplitude Modulation (MQAM) requires blind estimation of frequency offset and symbol rate at first. The traditional estimation algorithm of frequency offset based on multiple square spectrum and estimation algorithm of the symbol rate based on quadratic wavelet have better estimation performance. However, because of the fence effect of the Discrete Fourier Transform (DFT) and the influence of noise, the accuracy and reliability of estimation are limited. To solve these problems, a new frequency offset estimation method is proposed to reduce the impact of fence effect and improve the accuracy of frequency offset estimation and symbol rate estimation. A confidence criterion based on Signal to Noise Ratio (SNR) and spectral peak index is proposed to improve the reliability of frequency offset estimation. The simulation results based on QPSK and 16QAM show that the complexity of the improved algorithm is slightly higher than that of the traditional algorithm, but its performance is better than that of the traditional algorithm. It can effectively improve the estimation accuracy and reliability of frequency offset estimation and symbol rate estimation. 16QAM and QPSK have similar performance trends, but 16QAM need higher SNR in order to achieve the same performance as QPSK. The algorithm is robust and has good application value.