In this paper, quasi-ARX wavelet network (Q-ARX-WN) is proposed for nonlinear system identification. There are mainly two contributions are clarified. Firstly, compared with conventional wavelet networks (WNs), it is equipped with a linear structure, where WN is incorporated to interpret parameters of the linear ARX structure, thus Q-ARX-WN prediction model could be constructed and it is easy-to-use in nonlinear control. Secondly, guidelines for network construction are well considered due to the introduction of WNs, and Q-ARX-WN could be represented in a linear-in-parameter way. Therefore, linear support vector regression (SVR) based identification scheme may be introduced for the robust performance. Moreover, in adaptive control procedure, only linear parameters are needed to be adjusted when sudden changes have happened on the nonlinear system, thus the controller can track reference signal quickly. The effectiveness and robustness of the proposed nonlinear system identification method are validated by applying it to identify a real data system and a mathematical example, and an example of nonlinear system control is given to show usefulness of the proposed model.