To combat multipath fading, conventional diversity reception methods combine the distinguishable orthogonal signals received over different channels, such as frequency diversity uses the difference carriers to form orthogonal transmitted signals, and Rake diversity uses the pseudorandom noise sequence to generate the orthogonal received signals. They require additional transmission bandwidth, high complexity of the baseband processing from the dedicated design for the modulated signal, or additional radio frequency front-ends and antennas of the transmitter or receiver. To improve the reception performance under the multipath channel and avoid the above problems, we present a quasi-Rake diversity (QRD) reception method for continuous phase modulations, which only modifies the receiver's baseband processing. Its diversity gain is achieved by combining the replicas of the transmitted signal from the various propagation paths, using a joint iterative equalization and detection algorithm implemented in a baseband processing module of the receiver. It is composed of two steps. Firstly, we separate the line-of-sight (LOS) signal from various paths using the multipath interference cancellation (MIC) algorithm. The LOS signal is equalized and detected iteratively. It outperforms equalizing of the overall received signal. Secondly, the signals from other rays are extracted following the same method without iteration. All the separated signals are combined through the maximum ratio principle. The convergence of the MIC-based equalization is discussed in theoretical and numerical analysis. It also demonstrates that equalizing the LOS signal has a lower mean square error than equalizing the overall received signal. The remarkable performance improvement of the QRD (at most 5 dB) is presented compared to the conventional receiver using state-of-the-art equalizers.