Nowadays, communication service under low SNR is developing. To achieve lower computing expense and better precision of the carrier synchronization system under low SNR, a new frequency and phase estimation algorithm is suggested. The received signal is firstly processed by FFT operation; carrier estimation model based on maximized trigonometric interpolating result of FFT spectrum is built. Precise estimating results of frequency and phase are achieved by resolving the model. Implement of the algorithm is also proved to reduce computing expense. Simulations indicate that the algorithm not only has high precision which approaches CRB bound closer, but also has low SNR threshold. Compared with Rife and Quinn Algorithm, the algorithm requires almost equal computing expenses but has much higher precision. Compared with three-spectrum technique, the algorithm has slight higher precision but requires only half computing expense. When compared with iterative carrier estimation algorithms, the algorithm has approximate precision but requires much fewer computing expense and processing delay.