To achieve the nonlinear structural behavior, there is a need to trace of their equilibrium path in the space of load-displacement. Truss systems are commonly implemented in several structural systems, including high-span bridges and bracing of the supporting structure of tall buildings. Our study adapts a two-step method with cubic convergence into an incremental-iterative procedure to analyze the geometric nonlinear behavior of trusses. The solution method is combined with the Linear Arc-Length path-following technique. To find the approximate root of nonlinear equation system in the two-step method, two formulas are used. Structures are discretized using the Positional Finite Element Method and all truss bars are assumed to remain linear elastic. The correction of the nodal coordinates subincrement vector is performed using the Normal Flow technique. A computational algorithm was implemented using the free program Scilab. Our numerical results show that, when compared to the standard and modified Newton-Raphson algorithms, the new algorithm decreases the number of iterations and the computing time in the nonlinear analysis of trusses. Equilibrium paths with force and/or displacement limit points are obtained with good precision.