The inter-turbine burner (ITB) engine, which is introduced ITB between high and low pressure turbines, is a relatively new concept for increasing specific thrust and lowering high altitude specific fuel consumption (SFC) than engine with afterburner. While ITB engine brings outstanding performance improvement, it also brings challenges to the ITB engine control law design under unknown matching mechanism and multi-constraint. In this study, a self-scheduling control law design method for ITB engine mode transition that takes into account the ITB ignition and flameout characteristics and cooling air volume is proposed. This method derives the control law based on the global optimal algorithm and SHAP-value (SHapley additive exPlanation) analysis method, which avoids manual analysis and reduces the number of adjustment of variable geometric components. An ITB transient model is established to verify the control laws under the switching of ignition and flameout modes. Both flow fluctuations do not exceed 2%, and thrust fluctuations do not exceed 4% and 2% respectively. During the transition between the two modes, at most one variable geometry component is adjusted.