For nonlinear channel distortions of chaos-based communication systems，based on the analysis of the theory of chaotic signal reconstruction and the characteristics of transversal filter and functional link neural network (FLNN)，a novel nonlinear adaptive equalizer with the architecture of combination of transversal filter and functional link neural network (CFFLNN) is proposed in this paper. The novel nonlinear equalizer fully utilizes faster convergence characteristics of transversal filter and the nonlinear approximation capability of FLNN by function expansion due to enhanced input space. Furthermore，the performance of the novel nonlinear adaptive equalizer is also improved. Finally，the proposed equalizer is designed and its adaptive algorithm is deduced by the low complexity normalized least mean square (NLMS) method. And an analysis of stability and convergence for the derived algorithm is provided. To illustrate the analysis，results obtained from the computer simulation are also provided for both linear and nonlinear channels in chaos-based communication system.