In this paper, the node-based smoothed finite element method is improved with linear strain functions (NS-FEM-L) and applied for contact analysis using triangular elements. The smoothed strains are formulated by a complete order of polynomial functions and normalized with reference to the central points of smoothing domains. They are one-order higher than those adopted in the finite element method (FEM) and the standard smoothed finite element method. When using linear functions to describe strains in smoothing domains, solutions are more accurate and stable. The contact interfaces are discretized by contact point pairs using a modified Coulomb frictional contact model. The contact problems are solved via converted into linear complementarity problems which can be tackled by using the Lemke method. Numerical implementations are conducted to simulate the contact behavior, including the bonding-debonding, contacting-departing and sticking-slipping. The effects of various parameters related to friction and adhesion are intensively investigated. The comparison of numerical results produced by the NS-FEM-L and those of the FEM-Q4 demonstrates the validity and efficiency of the proposed method.