The combustor is the core component of the scramjet engine, and stable combustion is the prerequisite for the efficient operation of the scramjet engine. At present, researchers premix the fuel and oxidant to improve the combustion performance of the combustor, thereby reducing the mixing time and improving the combustion efficiency. This study proposes a new method of supplementing oxygen at the trailing edge of the strut to enhance mixing and combustion. This paper studies the combustion stability of the combustor equipped with this strut. This paper conducts a series of large eddy simulations under the combustor inlet conditions of Ma = 2.8, Tt = 1680 K, and Pt = 1.87 MPa, and obtains non-reactive flow field and reactive flow field data. The results show that the injection of oxygen at the trailing edge of the strut has a significant positive effect on fuel mixing and combustion. The non-reactive flow field results show that the injection of oxygen dilutes the kerosene at the trailing edge of the strut and improves the mixing efficiency. The reactive flow field results show that only when the oxygen supplement mass ratio is above 0.03 can a stable overall flame be formed inside the combustor, and oxygen supplementation enhances the heat release of premixed combustion. The Ret-Da distribution shows that due to the good mixing at the trailing edge of the strut, mixing is no longer the reason that restricts the combustion process, the heat release increases significantly, and the high-temperature heat release zone at the trailing edge of the strut ignites other fuels to form a stable flame in the combustor.