Engine-generator set (EGS) is an important energy supply component of high-voltage microgrid in series hybrid electric powertrain (SHEP). Sustained and steady energy supply from EGS is one of the conditions for the balanced energy between supply and demand. In some high-power processes, the balanced energy would be broken and the dynamic speed of EGS would be out of expectation, which can result in unstable working states of EGS. If the unstable working states of EGS can be known prior, it is significant for the research of unstable state identification and avoidance. Predicting rotational speed of EGS can warn of the previous issue in advance, while the insufficient data of unstable states would encounter overfitting problems in common prediction methods, so it is a challenge to improve the prediction effect of dynamic speed and then accurately predict the unstable states. Base on the above problems, a physics-informed learning algorithm with adaptive mechanism is proposed for EGS rotational speed prediction in this paper. First, a prediction problem related to the stability of SHEP running state is studied, which is found from engineering knowledge. Second, a new mechanism is proposed for physics-informed learning algorithm, and the physical information adopted to learning algorithm is more selective. Third, a professional adaptive function is originally formed according to speed characteristics, which bridge the information between physics and learning algorithm. By importing the experimental data, the prediction accuracy of proposed method in one of the test cycles is better than the results of baseline methods, specifically 27.11% and 3.49%, 11.90% and 7.94%, 53.83% and 27.62%. In summary, the proposed method can have better predictions against other baseline methods.