This paper investigates a blind equalization scheme for the continuous phase modulated frequency shift keying (CPFSK) system that appeared in [4], based on a characterization of multipath on the FSK signals. The distortion on the phase demodulated FSK signals due to a multipath channel can be modeled as a linear time varying filtering. The time variation of the linear filter model is slow for a mild multipath channel and fast for a severe multipath channel. Therefore, the constant modulus algorithm (CMA), which is the most practical and popular blind equalization algorithm, is applied on the pre-demodulated signals in order to mitigate the severeness of the multipath channel. Since CMA cannot achieve perfect equalization of pre-demodulated signals due to the correlated nature of CPFSK signals, the demodulated signals still suffer from the distortion due to a relatively slow time varying filter. Thus, a decision directed LMS equalizer is deployed to the demodulated signal in order to track and mitigate the distortion due to the time varying filtering.