Abrasive water jet cutting has been proven to be an effective technology for processing various engineering materials. To determine the optimal jet traverse rate (cutting speed) in abrasive water jet cutting is not very easy. This paper presents the application of an adaptive wavelet network (AWN) for overcoming this prediction problem. In this work, we consider some parameters such as change of focusing nozzle diameter, abrasive flow rate, jet pressure and depth of cut in order to control the abrasive water jet cutting process. The AWN model is adopted from an adaptable neuro-fuzzy inference system which is a Sugeno type fuzzy system that puts in the framework of this kind of systems to facilitate learning and adaptation. For model accuracy, we present to train an AWN by a hybrid learning method through a least square estimation with gradient based optimization algorithm to obtain the optimal translation and dilation parameters of the AWN. The effectiveness of the proposed approach is evaluated by the experimental data to estimate the cutting speeds for titanium and the model data is compared with the desired results. The predicted results indicated that the model can be used to identify jet traverse rates with an acceptable range of application for smooth cutting.