A hybrid accelerated model with two step length parameters for solving unconstrained optimization problems is presented. Applied hybridization process involves an efficient three term hybrid method. The accelerated double step size model is taken as guiding operator in this hybridization process. Defined method is convergent on the set of uniformly convex functions as well as on the set on strictly convex quadratics. We display a Dolan Moré performance profiles of derived iteration and of some other comparative hybrid and accelerated methods regarding the number of iterations and the number of function evaluations metrics. Displayed numerical test results confirm that derived model keeps a good properties of its forerunner method and outperform other comparative hybrid accelerated schemes