Aero engine condition monitoring (ECM) is essential in terms of improving availability and reducing life-cycle costs of the aero engine. Aero engine exhaust gas temperature (EGT) plays the most critical role in the ECM. By monitoring the EGT, maintenance crews can realize the aero engine health condition and speculate about the latent faults of the aero engine in advance. But it is difficult for traditional methods to predict the tendency of the EGT. So, a new model of hybrid recurrent process neural network (HRPNN) is proposed. The HRPNN acquires hidden-to-hidden and output-to-hidden feedbacks by introducing respectively the context units with self-feedback connections, and its inputs are time-varied functions. Hence, it can represent more states of the complicated nonlinear dynamical system such as aero engine more directly. A learning algorithm base on resilient backpropagation (Rprop) is developed for the HRPNN. To simplify the learning algorithm, a set of appropriate orthogonal basis functions are introduced to expand the input functions and the connection weight functions of the HRPNN. The method validation is proved by a benchmark of the Mackey-Glass chaos time series prediction. A practical utilization of the aero engine EGT prediction also demonstrates this point in terms of aero engine condition monitoring, the results indicate HRPNN can be used as an efficient ECM tool.