The Conjugate Gradient Method (CG) is a numerical method for solving quadratic problems, which can be used to minimize any differentiable function. In this study, we have analyzed the efficiency of CG for quadratic problems and implemented a version of this method for nonlinear systems in the least-squares formulation. We have also prepared a geometric analysis of the convergence of its nonlinear version, in order to evaluate the dependence of its efficiency with the starting point.