A hybrid conjugate gradient (CG) method is proposed for solving unconstrained optimization problems. The direction of the method is a combination of a three-term conjugate descent (CD) and Fletcher-Reeves (FR) CG directions. Also, it is close to the direction of the mem-oryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. In addition, under the Wolfe-type line search, the global convergence of the method is established. Numerical experiments are conducted on some benchmark test problems and the results are reported to show the efficiency of the propose method compared with some existing methods. © 2026 Academic Center for Education, Culture and Research TMU.