A pre-cooled combined engine based on a closed helium (He) cycle offers high specific thrust and high specific impulse. Therefore, evaluation of the performance of such an engine is crucial for engine applications and key technology research. This study employs an analytical approach to investigate the effects of key parameters on the performance of a pre-cooled core engine, assuming a perfect gas model. The findings revealed that the specific thrust and specific impulse of the pre-cooled core engine are related to the pressurized coefficient of the airflow passage and equivalence ratio (ER). An increase in the pressurized coefficient leads to an increase in both specific thrust and specific impulse. However, within a certain range, although the specific thrust is positively correlated with the ER, the specific impulse is greatly reduced. With specific component parameters and a fixed thermodynamic cycle, a minimum ER exists, which satisfies the cycle-matching requirement. Moreover, the value of the minimum ER is related to the closed-cycle efficiency. For a pre-cooled core engine with a simple closed He cycle, the minimum ER is approximately 2.5–3.5.