In space optical communication, both communication terminals need to detect the deviation of the incident optical axis to ensure that the communication link is unblocked. However, the beacon light used by the optical antenna control system has a large loss after long-distance transmission, and is strongly disturbed by background light and dark current noise. So, the accuracy of spot detection of the four-quadrant detector(QD) is reduced. To solve this problem, according to QD operating characteristics and noise characteristics, a new method based on amplitude modulation and cyclic cross-correlation is proposed. Under the condition of low output signal to noise ratio(SNR) of QD, this method can accurately measure the photocurrent amplitude of each quadrant of QD and calculate the accurate spot position. Experiments results show that, when the output SNR of QD is -14.58 dB, the absolute error of this method is less than 0.012 mm, the effectiveness of the method is proved.