In the present study, a new modelling technique was developed for the modelling and analysis of hyperchaotic systems using an expert system based on wavelet decompositions and the Adaptive Neuro-Fuzzy Inference System (ANFIS). The success and superior properties of this new expert system were shown by applying the hyperchaotic Chen system which is a hyperchaotic system. The obtained expert system consists of two layers, including wavelet decomposition and ANFIS. Wavelet decomposition was used for extracting features in the first layer, and ANFIS was used for system modelling in second layer. Furthermore, HSPICE simulation of the hyperchaotic Chen system was carried out for comparison with the proposed expert system. The structure of the ANFIS was improved and trained in the MATLAB toolbox. Numerical simulations were used in this study. Five various data sets have been used to test the simulation speed of the proposed expert system and HSPICE. The obtained results show that the proposed expert system simulation has much higher speed and accuracy in comparison with HSPICE simulation. The proposed expert system can be simply used in software tools for the design and simulation of the hyperchaotic Chen system and other hyperchaotic systems.