In this paper, numerical simulation of flow around a cylinder using the feedback force immersed boundary method is carried out. The feasibility of algorithm is verified by the numerical simulation of flow past two cylinders in tandem arrangement. The Cartesian adaptive mesh refinement is used in the whole flow field, and the dynamic distribution characteristics of flow field around a single cylinder and double cylinders are obtained when Re=100. Compared with the results in other literatures, the simulation shows a good agreement.