The interaction between fluid and immersed solid is a nonlinear multi-physical phenomenon in science and engineering. Due to the challenges of large structural deformation, topological changes in the fluid domain, complexity of the geometry of the structure and computational efficiency and robustness for simulating fluid structure interaction (FSI) problems, developing accurate and efficient finite element numerical methods has always been a research focus in the field of computational fluid dynamics. To overcome these difficulties, we present an efficient stabilised immersed framework involving finite element method called CutFEM and a second-order accurate staggered numerical scheme for fluid–solid coupling. In the following work, we apply this novel framework of computational FSI to several numerical examples to verify the efficiency and robustness of the proposed scheme, and the accuracy is also validated by the results by using the present scheme compared with the reference values.