Time series prediction plays an important role in engineering applications. Artificial neural networks seem to be a useful tool to solve these problems. However, in real engineering, the inputs and outputs of many complicated systems are time-varied functions. Conventional artificial neural networks are not suitable to predicting time series in these systems directly. In order to overcome this limitation, a parallel feedforward process neural network (PFPNN) is proposed. The inputs and outputs of the PFPNN are time-varied functions, which makes it possible to predict time series directly. A corresponding learning algorithm for the PFPNN is developed. To simplify this learning algorithm, appropriate orthogonal basis functions are selected to expand the input functions, output functions and network weight functions. The effectiveness of the PFPNN and its learning algorithm is proved by the Mackey-Glass time series prediction. Finally, the PFPNN is utilized to predict exhaust gas temperature time series in aircraft engine condition monitoring, and the simulation test results also indicate that the PFPNN has a faster convergence speed and higher accuracy than the same scale multilayer feedforward process neural network.