A simple and easy to implement but very effective algorithm for solving real-value parameter optimization problems is introduced in this paper. The main idea of the algorithm is to perform a local search repeatedly on a prospective subregion where the optimal solution may be located. The local search randomly samples a number of solutions in a given subregion. If a new best-so- far solution has been found, the center of the search subregion is moved based on the new best-so-far solution and the size of the search subregion is gradually reduced by a predefined shrinking rate. Otherwise, the center of the search is not moved and the size of the search subregion is reduced using a predefined shrinking rate. This process is repeated for a number of instances so that the search is focused on a gradually smaller and smaller prospective subregion. To enhance the likelihood of achieving an optimal solution, many rounds of this repeated local search are performed. Each round starts with a smaller and smaller initial search space. According to the experiment results, the proposed algorithm, though very simple, can outperform some well-known optimization algorithms on some testing functions.