The heavy-duty gas turbine is playing an increasingly significant role on power generation due to its lower-emission, higher flexibility and thermo-efficiency. Main subsystems of the gas turbine like compressor, combustor and turbine degrade over the operating time under the harsh environmental conditions, which largely impacts the efficiency and productivity of the system. Therefore, it is critical to develop effective approaches to monitor performance degradation of a heavy-duty gas turbine for system predictive maintenance thus improving the efficiency and productivity of the machine. This paper presents a new physics informed machine learning methodology to predict the degradation of gas turbine by seamlessly integrating thermodynamic heat balancing mechanism, component characteristics, multi-source data and artificial neural network model. The mechanism-based thermodynamic model is established for multiple subsystems considering the balance of flow, mass and energy, and then integrated to a system level for performance simulation of the gas turbine under different conditions. The system model is able to effectively simulate values for those parameters that are not measurable (e.g. GT exhaust flow) or inaccurately measured (e.g. fuel flow). Machine learning based data cleaning approach is employed to preprocess the multivariate raw data of the gas turbine. The difference between design performance data and corrected value obtained from the physics-informed model under ISO conditions is utilized to assess the performance degradation. A Long Short-Term Memory (LSTM) model is established from the fusion of the actual and simulation data to predict the performance degradation of the gas turbine. A comparison study with the classical Nonlinear Autoregressive Network with External Input (NARX) neural network is conducted to demonstrate the advantage of the proposed method. Key Word: Gas Turbine, Thermodynamic Balance, Performance Degradation Predict, Machine Learning, LSTM