Abstract: A frequency offset correcting algorithm is presented for frequency estimation of sinusoid signal, and a fast and accurate recursive algorithm for frequency estimation of sinusoid signal is investigated by associating the advantage of high accuracy of the M-Rife algorithm and the advantage of small computational load of the frequency offset correcting algorithm. Firstly, an initial estimation is obtained by the M-Rife algorithm for a truncated signal series which has a few points. Next, with the initial estimation result, a more accurate estimation is obtained by the frequency offset correcting algorithm for a longer truncated signal series. And then, deduce the rest by analogy. Finally, the ultimate estimation is obtained by the M-Rife algorithm for the entire signal series. The computational complexity of the recursive algorithm is lower than that of an FFT operation when the signal series is long. Simulation results show that the performance of this algorithm is stable, and the estimation variance is nearly the same as the M-Rife algorithm, approaching to CRLB(Cramer-Rao Lower Bound). The algorithm is convenient for realizing real-time frequency estimation accurately.