A hybrid genetic algorithm (HGA) combines a genetic algorithm (GA) with an individual learning procedure. One such learning procedure is a local search technique (LS) used by the GA for refining global solutions. A HGA is also called a memetic algorithm (MA), one of the most successful and popular heuristic search methods. An important challenge of MAs is the trade-off between global and local searching as it is the case that the cost of a LS can be rather high. This paper proposes a novel, simplified, and efficient HGA with a new individual learning procedure that performs a LS only when the best offspring (solution) in the offspring population is also the best in the current parent population. Additionally, a new LS method is developed based on a three-directional search (TD), which is derivative-free and self-adaptive. The new HGA with two different LS methods (the TD and Neld-Mead simplex) is compared with a traditional HGA. Two benchmark functions are employed to illustrate the improvement of the proposed method with the new learning procedure. The results show that the new HGA greatly reduces the number of function evaluations and converges much faster to the global optimum than a traditional HGA. The TD local search method is a good choice in helping to locate a global “mountain” (or “valley”) but may not perform as well as the Nelder-Mead method in the final fine tuning toward the optimal solution.