In this work, an effective and stable immersed cell-based smoothed finite element method (ICS-FEM) together with mean value coordinate (MVC) projection using quadrilateral elements is presented for 2D fluid-structure interaction (FSI) problems. As an immersed-based algorithm, the entire system is divided into three components: large-deformed nonlinear structure, incompressible viscous fluid, and fictitious fluid part for FSI force [1-3]. A characteristic-based split (CBS) CS-FEM solver is developed to solve the Navier-Stokes (N-S) equation. An explicit total Lagrange (TL) CS-FEM solver is utilized to depict the large deformation of the elastic structure. A function with the pressure and viscous force on the interface is applied to obtain the FSI force in the fictitious fluid. The problem domains are discretized into a set of bilinear quadrilateral elements and four cell-based smoothing domains are constructed for each element. The cell-based smoothing operation instead of the traditional mapping operation of iso-parametric elements are executed to all gradient-related terms for both structure and fluid. A method based on the MVC is used for the interpolation process and the search criterion during the loops to traversal element-node pairs. The results of numerical examples demonstrate the advance of the proposed method, including computational precision, convergence rate, robustness, etc.