In our previous research, we proposed a serial unequal error protection (UEP) code system for use with information sources that contain a mixture of both important and less important data. Previously, theoretical analyses were presented, and the effectiveness and the validity of the system for additive white Gaussian noise (AWGN) channels were confirmed using theoretical analyses and computer simulations. On the other hand, we proposed an adaptive error prediction filter with a decision feedback equalizer (AEPF-DFE) to achieve faster convergence and lower computational cost during the tracking period. In this paper, we proposed our UEP system using AEPF-DFE for time and frequency selective fading channels. We confirmed the improvement in BER performance and the effectiveness of adaptive equalization for the proposed system in fading channels. Also, we confirmed the predominance of the proposed system by comparing the previous scheme, that is, the case using a simple DFE.