This paper is concerned with near-optimal source search problem using a multiagent system in cluttered indoor environments. The goal of the problem is to maximize the detection probability within the minimum search time. We propose a two-stage strategy to achieve this goal. In the first stage, a greedy approach is used to define a set of grid cells with the aim of maximizing the detection probability. In the second stage, an iterative branch-and-bound procedure is used to design the search paths of all agents so that all grid cells are visited by one agent and the largest search path among all agents is minimized. Simulation results show that the proposed search algorithm has better performance in terms of exploration time compared to other existing methods.