Direct sequence spread spectrum (DSSS) using continuous phase modulation (CPM) inherits the techniques' benefits, constant envelope, anti-interference, and spectral efficiency. To get diversity gains over a Rayleigh-fading multipath channel as in conventional direct sequence spread-spectrum binary phase shift keying (DSSS-BPSK) system, a new class of coherent RAKE receivers is proposed in this work. By introducing chip branch metric to the receiver scheme, despreading and data detection can be done meanwhile based on Maximum Likelihood Sequence Detection (MLSD). Compared to the conventional RAKE receiver which sums decision metrics symbol-by-symbol, the proposed DSSS-CPM RAKE receiver accumulates symbol branch metric increments over every phase state of multiple paths after chip phase synchronization. Numerical results show that DSSS-CPM using the synchronous despreading and demodulation algorithm has no performance loss compared to CPM system that employs MLSD algorithm under the same test conditions. Moreover, the proposed RAKE receiver outperforms conventional RAKE receiver and achieves a remarkable diversity gain of bit error rate (BER) under the Rayleigh-fading multipath channel.