This letter presents a novel stepwise multi-agent task planning method that incorporates neighborhood search to address large-scale problems, thereby reducing computation time. With an increasing number of agents, the search space for task planning expands exponentially. Hence, conventional methods aiming to find globally optimal solutions, especially for some large-scale problems, incur extremely high computational costs and may even fail. In this letter, the proposed method easily achieves the goals of multi-agent task planning by solving an initial problem using a minimal number of agents. Subsequently, tasks are reallocated among all agents based on this solution and the solutions are iteratively optimized using a neighborhood search. While aiming to find a near-optimal solution rather than an optimal one, the method substantially reduces the time complexity of searching to a polynomial level. Moreover, the effectiveness of the proposed method is demonstrated by solving some benchmark problems and comparing the results obtained using the proposed method with those obtained using other state-of-the-art methods.