In this paper, a parametric variational principle for van der Waals force simulation between any two non-bonded atoms is established together with the corresponding improved quadratic programming method for numerical simulation of mechanical behaviours of carbon nanotubes. Carbon-carbon covalent bond interaction in carbon nanotubes is modeled and computed based on molecular structural mechanics model. Van der Waals force is simulated by the network of bars with a special nonlinear mechanical constitutive law in the finite element analysis. In comparison with conventional numerical methods, the suggested method does not depend on displacement and stress iteration, but on the base exchanges in the solution of a standard quadratic programming problem. Thus, the model and method developed exhibit very good convergence behavior in computation and provide accurate predictions of the mechanical behaviours and displacement distributions in the nanotubes. Numerical results demonstrate the validity and the efficiency of the proposed method.