Based on the study of the performance of Rife and Quinn algorithms, an improved algorithm is proposed to solve the problems of the fluctuating accuracy and weak anti-noise ability in traditional frequency offset estimation algorithm. This algorithm combines the precision advantage of the Rife algorithm when dealing with large frequency offset factors with the stability of the Quinn algorithm. It also employs multi-spectral-line interpolation with added weighting coefficients to overcome the problem of misjudging the correction direction when the actual frequency is close to the quantized frequency points. Experimental results demonstrate that the proposed algorithm can maintain high frequency estimation accuracy even under low signal-to-noise ratio (SNR) conditions, exhibiting overall more stable performance and closer approximation to the Cramér-Rao lower bound (CRLB) compared to other similar algorithms. Finally, the algorithm was deployed on an FPGA platform, and the results were compared and analyzed with the actual signal frequency, revealing a maximum root mean square error (RMSE) of approximately 16  Hz.