This paper mainly studies the optimal control problem of turbine-based combined cycle (TBCC) engines in the mode-transition stage. Based on the TBCC scheme proposed by Xiamen University, an aerothermodynamic model is established as a verification model for the validity of control laws. To reduce the complexity of control design, a control-oriented linear parameter-varying (LPV) model with Mach number as a scheduling variable is established under a given flight path. The design of mode-transition points and distribution of air-flow-rate among paths during the mode-transition process are transformed into linear quadratic (LQ) optimal control problems for an LPV system under the initial and terminal as well as process constraints. By optimizing the opening of the splitters of the inlet and the fuel flow in each channel, the optimal mode-transition points are found to achieve coordinated control and complete the high-precision thrust tracking during the mode-transition process.