Accurate frequency offset estimation is the key to correct receiving of low-Earth-orbit (LEO) satellite signals. Under the circumstances of low signal-to-noise ratio (SNR) and large frequency offset, conventional estimation algorithms for frequency offset are limited by their estimation range and/or SNR threshold, for which reason the estimation accuracy cannot achieve the ideal error probability. Based on joint iterative method, this study proposes an improved joint estimation algorithm for frequency offset. Specifically, the coarse estimation stage takes advantage of the wide estimation range of M&M algorithm, thereby enlarging the estimation range of the proposed algorithm while improving the estimation accuracy of the M&M algorithm through conducting iterative estimation. The fine estimation stage integrates the high estimation accuracy of L&R algorithm to capture the residual frequency offset after accomplishing the coarse estimation, reducing the estimation error within low SNR region while lowering the SNR threshold of the proposed algorithm. The simulation results suggest that the proposed algorithm outperforms the commonly used conventional ones in estimating the frequency offset of LEO satellite signals with wide estimation range and low SNR threshold.