An effective algorithm is presented for estimating carrier frequency offset of Amplitude Phase Shift Keying(APSK) modulated signal. The data of the signal is obtained after the process of timing synchronization. The algorithm is based on the characteristic that the radiuses of the points of the constellation of APSK modulated signal are different. The value of the data is set to zero except the points with the smallest radius. The spectrum line of the quartic spectrum of the zeroing data is extracted to estimate carrier frequency offset. Simulation results show that this algorithm has low complexity and high practicality. The mean square error of the estimation of carrier frequency offset is below -80 dB when the number of symbol is 500 and the signal to noise ratio is above 15 dB.