The multiple sequence alignment problem is one of the important problems in Genome Informatics. The notable feature of this problem is that its state-space forms a lattice. Researchers have applied search algorithms such as A* and memory-bounded search algorithms including SNC to this problem. Unfortunately, previous work could align only seven sequences at most. Korf proposed DCBDS, which exploits the features of a grid, and suggested that DCBDS probably solved this problem, effectively. We found, however, that DCBDS was not effective for aligning many sequences. In this paper, we propose a simple and effective search algorithm, A* with Partial Expansion, for state-spaces with large branching factors. The aim of this algorithm is to store only necessary nodes for finding an optimal solution. In node expansion, A* stores all child nodes, while our algorithm stores only promising child nodes. This mechanism enables us to reduce the memory requirements during a search. We apply our algorithm to the multiple sequence alignment problem. It can align seven sequences with only 4.7% of the stored nodes required by A*.