Multi index continuous phase modulation （Multih CPM） has attracted attention for its continuous phase，constant envelope，high frequency and bandwidth utilization rate ，but its demodulation requires a large number of matched filters and grid state，which limits its application in engineering.Therefore，we can reduce the use of the number of matched filters and grid state in Viterbi decoding，by using Laurent decomposition and approximate process.Compared with the maximum likelihood sequence detection method，Laurent decomposition can greatly reduce the number of matched filters and grid states.The simulation results show that the complexity of the demodulation is obviously reduced in the case of little performance loss.