In this paper, we propose a real-time moving target search algorithm for dynamic and partially observable environments, modeled as grid world. The proposed algorithm, Real-time Moving Target Evaluation Search (MTES), is able to detect the closed directions around the agent, and determine the best direction that avoids the nearby obstacles, leading to a moving target which is assumed to be escaping almost optimally. We compared our proposal with Moving Target Search (MTS) and observed a significant improvement in the solution paths. Furthermore, we also tested our algorithm against A^* in order to report quality of our solutions.