Multi-h Continuous Phase Modulation (CPM) has a constant envelope with periodical modulation indices, and its spectral efficiency and power efficiency are higher than single-h CPM. However, the receiver complexity also increases exponentially. In this paper, a combination of Tilde Phase, Frequency Pulse Truncation, and State Space Partition is proposed to reduce the complexity of Multi-h CPM, which reduces the phase state from 512 to 16 with a theoretical loss of about 0.8dB. Meanwhile, the reduced-complexity demodulation algorithm is verified on FPGA. The simulated and online BER results are close to the theoretical analysis curve, and the implementation resource usage is reduced by 59% compared to the conventional 128 states demodulation algorithm.