Mathematical models, in which many input variables are involved, require a range of input and output data, since the number of parameters increases with the input variables. GMDH (Group Method of Data Handling) has been used for the identification of a mathematical model that has many input variables but limited data needs by using a hierarchical structure. This paper proposes a neuro-fuzzy GMDH model, adopting Gaussian radial basis functions (GRBF) as partial descriptions of GMDH. GRBF is reinterpreted as both a simplified fuzzy reasoning model and as a three-layered neural network. As an example of applying the algorithm, the wheel wear equation is identified, using data from experiments of abrasive cut-off. In the model, characteristics of work materials, grinding fluids, factors of wheels, wheel velocity and table feed are used as input variables, and the grinding ratio is the resulting output. The validity of the model is confirmed within the predicted accuracy by using additional data.