Abstract: A new super-memory gradient method for solving unconstrained optimization problems was proposed. A new search direction was generated by using the current and previous multi-step iterative information in the proposed method, and the step-size at each iteration was defined by a curve search rule, which can be used to solve large scale unconstrained optimization problems because it avoids the computation and storage of some matrices. Furthermore, the global convergence and the convergence rate of the new algorithm were proved under some weak conditions. Finally, numerical results showed that the proposed algorithm is effective