The turbine-based combined cycle (TBCC) engine is a desirable propulsion system for airbreathing hypersonic flight vehicles, which is also a type of unmanned aerial vehicle, especially when considering about horizontal taking off and landing. However, the TBCC engine faces a typical situation of “thrust gap” during the turbojet-to-ramjet mode transition process, causing thrust drops considerably. To pursue smooth thrust transition, an anti-disturbance control strategy with bypass introduced for mode transition is proposed after building the dynamic performance model of an over-under TBCC engine in this work. First, extra airflow is injected into the ramjet flow path from the bypass system to satisfy the thrust requirement, and the airflow amount needs to be precisely determined. Correspondingly, a quantitative decision-making method is proposed by establishing a decision model using neural networks to calculate the bypass airflow requirement. In this way, directly solving the solution from the forward highly nonlinear model of ramjet thrust is circumvented. Second, the ramjet thrust controller is designed by extension of an improved active disturbance rejection control (ADRC) method with fuel saturation and combustion delay considered. Simulations of the overall process show that the mode transition control system with bypass introduced can achieve a smooth transition of thrust with the maximal total thrust reduction of 0.49%, which is preferable. The improved ADRC thrust controller has a satisfying tracking performance of thrust commands and good robustness against model uncertainty and external disturbances. The mode transition control strategy provided can effectively improve the mode transition performance of the over-under TBCC engine.