In this paper, the dual mode error correcting adaptive decoding algorithm which is adapted to the continuous phase frequency shift keying(CPFSK) modulation is presented as a technique for overcoming the distortion that reveals from the Rayleigh fading channel. The dual mode adaptive decoder nominally operates as a Viterbi decoder and switches to the burst error correcting mode, whenever the decoder detects an uncorrectable burst error pattern. Under the fading channel environment and when the usable memory quantity is restricted, the dual mode adaptive decoding algorithm shows an advantage in the BER performance over the interleaving technique, and also obtains the merit of not needing the large time delay that the interleaving technique requires. The experimental results from the computer simulation demonstrate the performance of the algorithm and verify the theoretical results.