Tensegrity systems are lightweight structures composed of cables and struts. The nonlinear behavior of tensegrity systems is critical; therefore, the design of these types of structures is relatively complex. In the present study, a practical and efficient approach for geometrical nonlinear analysis of tensegrity systems is proposed. The approach is based on the point iterative method. Static equilibrium equations are given in nodes for subsystems, thus the maximum unknown displacement number in each step is three. Pre-stress forces in the system are taken into account in a tangent stiffness matrix, while similar calculations are carried out for each node in the system which has a minimum of one degree of freedom. In each iteration step, the values found in previous steps are used. When it reaches permissible tolerance of calculation, final displacements and internal forces are obtained. The structural behavior of the tensegrity systems were evaluated by the proposed method. The results show that the method can be used effectively for tensegrity systems.