Abstract: In this study, we present a new search direction known as the CG-Broyden method which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden’s family method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-Broyden method is more efficient than the ordinary Broyden method. Besides, we also prove that the new algorithm is globally convergent.