Machine learning (ML) methods are becoming popular in prognostics and health management (PHM) of engineering systems due to the recent advances of sensor technology and the prevalent use of artificial neural networks. In practice, mechatronic systems are by nature, prone to degradation/failure due to complex failure mechanisms and other unknown causes. As a result, degradation modeling and prediction of mechatronic systems are quite challenging especially when highly integrative and special operational conditions are considered. To overcome such challenges, artificial neural networks can be employed. This paper proposes the use of a long short-term memory (LSTM)-based multi-input neural network for degradation modeling and prediction of an Electro-Hydrostatic Actuator (EHA) system. The failure mechanisms of the EHA system are explored first, and the obtained physics-of-failure information is utilized in constructing the LSTM neural network to enhance the prediction capability of the model. An actual dataset collected from an EHA test bench is utilized to illustrate the effectiveness of the proposed physics-informed LSTM method for modeling the EHA system's degradation behavior. The result shows that the proposed method provides more accurate life prediction than several benchmark methods for the EHA system.