The air compression ratio in a modern aero engine has been significantly increased to enhance the engine’s thermal efficiency, thereby leading to high-pressure combustion with the combustor pressure exceeding the fuel’s critical pressure (~23 atm for the aviation kerosene). In this work, large eddy simulations are conducted to investigate the effects of two air swirling injection on the turbulent flow and combustion of kerosene-air in a dual-swirl model combustor at a supercritical pressure of 4 MPa. The flamelet progress-variable (FPV) model is applied to handle turbulent combustion, and the extended corresponding states (ECS) method is adopted to evaluate the thermophysical property variations at the high pressure. Results indicate that the inner air swirler controls the mixing process and chemical reactions inside the injector. The precessing vortex core (PVC) is generated by the inner swirling flow, and the PVC frequency increases significantly as the inner air swirler angle varies from 25° to 40°. On the other hand, the outer air swirler exerts strong impacts on the flow field and flame characteristics in the combustor. As the outer air swirler angle increases, the PVC frequency decreases at a moderate inner air swirler angle. A modified Strouhal number is proposed, and the detailed analyses reveal that the PVC frequency is influenced by the swirl number and the maximum axial velocity in the inner injector. Results obtained herein would help gain fundamental understanding on swirling flow and flame dynamics at high pressures.