This paper first calculates numerically the Symmetric Information Rate (SIR) of Cotinuous Phase Modulation (CPM) schemes over Additive White Gaussian Noise (AWGN) channel, modeling CPM and channel as a Memory-less Modulator (MM) plus a Markov Finite State Channel (FSMC),then proposes an optimal detector, which is of BCJR based Decision Feedback Detector (DFD) but non-iterative. It can achieve the SIR as the sequence length approaches infinity while the complexity is extremely low. Finally, both theoretic proof and numerical simulation are performed to show the optimality. Simulation results show that it nearly achieves the theoretic bound and outperforms the Viterbi Detector (VD) with 2dB in low Eb/N0.