Existing fusion-based local community detection algorithms have achieved good results. However, when assigning a node to a community, similarity functions are sometimes used, which only use node information, while ignoring connection information within the community. These algorithms sometimes fail to find influential nodes, which eventually leads to the failure to find a complete local community. To address these problems, a new local community detection algorithm is proposed in this article. Two strategies, of strong fusion followed by weak fusion, are used alternately to fuse nodes. Compared with using two fusion strategies alone, the alternating loop method can improve the solution of the algorithm in each stage. In strong fusion, we propose a new membership function that considers both node information and connection information in the local community. This improves the quality of the fused node while preserving the structure of the current community. In weak fusion, we propose a parameter-based similarity measure, which can detect influential nodes for a local community. We also propose a local community evaluation metric, which does not require true division to determine the optimal local community under different parameters. Experiments, compared to six state-of-the-art algorithms, show that the proposed algorithm improves accuracy and stability, and also demonstrate the effectiveness of the new local community evaluation metrics in parameter selection.