In contact analysis, reducing the computing time has been an issue under the premise of ensuring calculation accuracy around the region with violent stress changes. To improve computational efficiency for contact analysis in flexible multibody system, this paper proposes an adaptive local mesh refinement and coarsening approach based on analysis-suitable T-splines (ASTS). First, the kinematic model of thin plate is established based on analysis-suitable T-spline surface, and large deformation of flexible thin plate is described by the elastic model created by nonlinear Green–Lagrange strain. Second, to reduce computing time in contact analysis and ensure analysis accuracy, based on contact state and refinement distance, an effective adaptive local element mesh update method is proposed, which only refine locally on subject's refinement region and integrate redundant elements to reduce the degree-of-freedom (DOF) of system. Third, to analyze the system with varying mesh, a new solving algorithm with dynamic variables and geometry update routine is developed. Finally, performance of the proposed method in static and dynamic simulation is validated by four numerical examples. Results and consuming time of ASTS-based varying mesh prove the feasibility of the proposed method in contact problems.