In this letter, a new and accurate frequency estimation method of complex exponential signals is proposed. The proposed method divides the signal samples into several identical segments and sums up the samples belonging to the same segment respectively. Then it utilizes fast Fourier transform (FFT) algorithm with zero-padding to obtain a coarse estimation, and exploits three Fourier coefficients to interpolate a fine estimation based on least square error (LSE) criterion. Numerical results show that the proposed method can closely approach the Cramer-Rao bound (CRB) at low signal-to-noise ratios (SNRs) with different estimation ranges. Furthermore, the computational complexity of the proposed method is proportional to the estimation range, showing its practical-oriented ability. The proposed method can be useful in several applications involving carrier frequency offset (CFO) estimation for burst-mode satellite communications.