Since gas turbine plays a key role in electricity power generating, the requirements on the safety and reliability of this classical thermal system are becoming gradually strict. With a large amount of renewable energy being integrated into the power grid, the request of deep peak load regulation for satisfying the varying demand of users and maintaining the stability of the whole power grid leads to more unstable working conditions of gas turbines. The startup, shutdown, and load fluctuation are dominating the operating condition of gas turbines. Hence simulating and analyzing the dynamic behavior of the engines under such instable working conditions are important in improving their design, operation, and maintenance. However, conventional dynamic simulation methods based on the physic differential equations is unable to tackle the uncertainty and noise when faced with variant real-world operations. Although data-driven simulating methods, to some extent, can mitigate the problem, it is impossible to perform simulations with insufficient data. To tackle the issue, a novel transfer learning framework is proposed to transfer the knowledge from the physics equation domain to the real-world application domain to compensate for the lack of data. A strong dynamic operating data set with steep slope signals is created based on physics equations and then a feature similarity-based learning model with an encoder and a decoder is built and trained to achieve feature adaptive knowledge transferring. The simulation accuracy is significantly increased by 24.6% and the predicting error reduced by 63.6% compared with the baseline model. Moreover, compared with the other classical transfer learning modes, the method proposed has the best simulating performance on field testing data set. Furthermore, the effect study on the hyper parameters indicates that the method proposed is able to adaptively balance the weight of learning knowledge from the physical theory domain or from the real-world operation domain.