A type of wavelet neural network, in which the scale function is adopted only, is proposed in this paper for non-linear dynamic process modelling. Its network size is decreased significantly and the weight coefficients can be estimated by a linear algorithm. The wavelet neural network holds some advantages superior to other types of neural networks. First, its network structure is easy to specify based on its theoretical analysis and intuition. Secondly,network training does not rely on stochastic gradient type techniques and avoids the problem of poor convergence or undesirable local minima. The excellent statistic properties of the weight parameter estimations can be proven here. Both theoretical analysis and simulation study show that the identification method is robust and reliable.Furthermore, a hybrid network structure incorporating first-principle knowledge and wavelet network is developed to solve a commonly existing problem in chemical production processes. Applications of the hybrid network to a practical production process demonstrates that model generalisation capability is significantly improved.