Pulse position modulation (PPM) is the most often used modulation technique in space laser communications. As avalanche photodiode detector (APD) has high gain, high sensitivity and fast response, it is a likely candidate to detect laser signals for providing space laser communications needs. This paper discusses the characteristics and sorts of noises in the APD signal detecting subsystem, as the PPM channel is considered in the space laser communication system. Based on the ability of achieving topical characteristics of signals by the wavelet transform, a method of APD signal detecting based on the wavelet analysis is proposed. Four different threshold limit-selecting methods are applied to choose the wavelet coefficient for signal-recovering. A primary simulation experiment and some analyses are also done. The results show that the adaptive threshold values selecting algorithm is the best one. It can mitigate the effect of the intensive background noise to improve the performance of the APD signal detecting system.