A procedure based on an adaptive grid embedding technique is proposed in the present paper to simulate the complex flow fields induced by the interactions between supersonic jets and external flows. The proposed procedure utilizes the high-resolution TVD scheme for solving the local flow field where flow parameters are found to vary drastically, and any conventional second-order scheme can be used to solve the problem in the remaining region. To serve the purpose, a single-dimensionally adapting technique is developed and applied successively, in conjunction with the Strang-type splitting scheme, to solve the multi-dimensional gas dynamic equations.As a demonstration, solutions of the Euler equations for a flow of supersonic jet interacting with an external flow computed using the adaptive grid technique developed in this work, as well as the conventional TVD procedure, are presented in this paper. The numerical results reveal that the present technique is capable of providing visualizations of complex flow fields with high resolution. Yet, through comparisons, it is also found to be highly efficient.