The oscillations of the flow field around a hemispherical nose with a supersonic opposing jet in a free stream of Mach 3.98 are computed. Two total pressure ratios of a jet to a free stream 0.2 and 0.6 are examined, which correspond to unsteady flow and steady flow, respectively. The axisymmetric Navier-Stokes equations with Shear-Stress Transport (SST) turbulence model are used as the governing equations in this paper. The oscillations of the flow field are reproduced, and mechanism of the oscillations is analyzed. Time-accurate algorithm is found to be necessary when an opposing jet flow field is solved, even for stable flow field. The time-averaged density distribution obtained in this paper is in good agreement with schlieren photograph. Also, the wall heat flux predicted in this paper is in agreement with experimental result.