To improve the computational efficiency of the supersonic gas jet flow simulation, an efficient and accurate method for fast prediction of the flow field of supersonic gas jets is proposed based on the reduced order model (ROM) of the proper orthogonal decomposition (POD) and the back propagation neural network (BPNN). Firstly, the jet flow dataset containing multiple working conditions is constructed by high-fidelity CFD simulation, and the dominant modes of the flow field and their low-dimensional feature coefficients are extracted by the POD, so that the high-dimensional features of the original flow field are compressed into a low-dimensional orthogonal space within 20 dimensions. Subsequently, a back propagation neural network with operating parameters as inputs and modal coefficients as outputs is designed to directly establish a nonlinear mapping relationship between the input parameters and the low-dimensional features through end-to-end training. Finally, the flow field reconstruction is completed by modal superposition. The results show that, the developed method improves the efficiency of numerical simulation by nearly 100 times compared with the traditional CFD computation while maintaining the accuracy of predicting the velocity and temperature distribution of the flow field. The study provides an efficient tool for real-time analysis and optimization design of supersonic gas jets, and validates the potential of a data-driven downscaling mapping framework based on complex flow modelling.