An immersed boundary-discrete Boltzmann model (IB-DBM) is presented in this work for the simulation of flow around a blunt body with compressible flows. In this scheme, the immersed boundary method (IBM) is incorporated into the discrete Boltzmann model (DBM) through a force term, so that the fluid–solid interaction can be replaced by the external forces exerted on the fluid. In the IB-DBM model, the fluid Reynolds number and Mach number can be adjusted independently to facilitate the study of cylindrical flow characteristics in various compressible flows. The simulations of flow around a cylinder at different Reynolds and Mach numbers demonstrate that the streamlines do not intersect or penetrate each other, indicating the successful enforcement of the no-slip boundary condition. Furthermore, the results of relevant physical quantities have a good agreement with the data provided in the literature and capture some information about thermodynamic non-equilibrium effects. This work provides guidance and basis for further solving the problem of fluid–structure coupling in nuclear reactor engineering.