Practical optimization problems are often too complex to be formulated exactly. Knowing multiple good alternatives can help decision-makers easily switch solutions when needed, such as when faced with unforeseen constraints. A multimodal optimization task aims to find multiple global optima as well as high-quality local optima of an optimization problem. Evolutionary algorithms with niching techniques are commonly used for such problems, where a rough estimate of the optima number is required to determine the population size. In this paper, a partition-based random search method is proposed, in which the entire feasible domain is partitioned into smaller and smaller subregions iteratively. Promising regions are partitioned faster than unpromising regions, thus, promising areas will be exploited earlier than unpromising areas. All promising areas are exploited in parallel, which allows multiple good solutions to be found in a single run. The proposed method does not require prior knowledge about the optima number and it is not sensitive to the distance parameter. By cooperating with local search to refine the obtained solutions, the proposed method demonstrates good performance in many benchmark functions with multiple global optima. In addition, in problems with numerous local optima, high-quality local optima are captured earlier than low-quality local optima.