In order to get better speech enhancement effect for hearing aids when used in the environment with non-stationary or multiple noise, which will lead a sharp decline effect of user experience, a Coherent Filter Generalized Sidelobe Canceller (CF-GSC) speech enhancement algorithm based on small size microphone array was proposed. Aiming at the weak correlation noise which caused by the waves, fans and other approximate white noise, as well as the strong correlation noise caused by the point or other competitive sources, coherent filtering and traditional Generalized Sidelobe Canceller (GSC) structure were utilized to remove weak correlation and strong correlation noise separately, the Voice Activity Detection (VAD) algorithm was also applied during this process. The simulation results show that the proposed algorithm can obtain enhancement effect by almost 2 dB compared with the improved coherent filter and traditional generalized sidelobe canceller method under the environment of a variety of noise, meanwhile, the speech intelligibility also gets obviously improved.