Under the background of blind demodulation of Continuous Phase Modulation (CPM) signals, this paper extends the multiple-symbols differential demodulation, and makes an analysis of its principle, performance, and its tolerance to frequency offset, timing offset and modulation index offset. Its complexity of computation is also analyzed. The numeric computer simulation is presented. The results show that its BER performance improves with the amount of differential symbols. However the more differential symbols, the more computation. It has good tolerance to frequency offset, timing offset and modulation index offset. This algorithm can apply to the blind demodulator of CPM.