A new methodology for modelling of dynamic process systems, the output integrated recurrent neural network (OIRNN), is presented in this paper. OIRNN can be regarded as a modified Jordan recurrent neural network, in which the past values for certain steps of the output variables are integrated with the input variables, and the original input variables are pre-processed using principal component analysis (PCA) for the purpose of dimension reduction. The main advantage of the PCA-based OIRNN is that the input dimension is reduced, so that the network can be used to model the dynamic behavior of multiple input multiple output (MIMO) systems effectively. The new method is illustrated with reference to the Tennessee-Eastman process and compared with principal component regression and feedforward neural networks.