For highly maneuverable aircraft, the afterburning engine serves as a core and critical component. Due to the complex structure of the afterburner and the strong coupling among parameters, mechanism-based modeling of afterburning engines remains extremely challenging. To address this problem, this paper proposes a data-driven hybrid algorithm modeling framework for a light-duty afterburning turbojet engine. Using test-bench data from the TWP220L light-duty afterburning turbojet, two hybrid algorithm models were developed: (i) PSO-DNN and (ii) NGO-LSSVM. Four models, DNN, PSO-DNN, LSSVM, and NGO-LSSVM, were compared by mapping engine input parameters (altitude, Mach number, rotor speed, and fuel flow rate) to two key performance outputs (thrust and turbine pressure ratio). Based on visual error analysis and regression evaluation metrics, it was found that the optimized algorithm significantly reduced the prediction error. The NGO-LSSVM model achieved the highest accuracy in both performance indicators, increasing R² by 5.3% for thrust, and increasing R² by 6.8% for turbine pressure ratio. This framework offers a practical and high-precision approach for light-duty afterburning engine performance prediction and lays a foundation for the development of model-based and data-driven onboard control strategies.