Under the condition of supersonic incoming flow, a missile lateral jet flow field has complex flow structures, such as a strong shock wave, an unsteady vortex and flow separation. In order to improve ability to capture complex flow structures in numerical simulation of lateral jets, this paper proposes a combined-grid adaptive method. When combined with finite volume approximation of second-order and h-type adaptive technology, our method was verified by numerical experiments, which shows that wave structure and vortex structure in the jet flow field can be effectively captured at the same time. In comparison of uniformly refined mesh results, it was found that accuracy of computed results and resolution of characteristic flow structures were significantly improved after mesh adaptation. In comparison of the pressure coefficient, it was found that the error between the adaptive mesh and the uniformly refined mesh was smaller, and the maximum errors of the base grid, adaptive grid and uniformly refined grid were 92.1% and 12.3%.