This study proposes a novel node-to-segment (NTS) approach for modeling 2D frictionless contact problems within a cell-based smoothed finite element method (CS-FEM) framework. In this study, the smoothing domains created on top of the general quadrilateral element mesh can be further subdivided into one or several smoothing cells. Owing to converting area integration into the line integration, the construction of the smoothed strain field avoids the mapping of isoparametric coordinates thereby accommodating severely distorted quadrilateral elements. In addition, the reasons for the defects of the NTS discretization are analyzed in detail and a comprehensive solution based on the classical penalty method namely penalty homogenization method (PHM) is given. Various types of contact patch tests with high distortion and contact boundary meshes with different densities are examined completely. Numerical examples using straight boundaries and curved boundaries are presented to highlight the robustness and versatility of the overall approach.