In recent years, underwater acoustic target recognition has received considerable attention. However, due to the time-varying and space-varying nature of the underwater acoustic channel, as well as the complex and variable characteristics of the underwater target sound sources, water sound signal recognition tasks face significant challenges. Traditional methods for water sound signal recognition struggle to capture sufficient representation information of the targets and lack robustness against noise, resulting in suboptimal recognition performance. To address these issues, this study proposes a water sound signal recognition method based on the multi-branch external attention network (MEANet), which can effectively extract features and perform recognition in complex marine environments. MEANet consists of multiple branches for the backbone network, channel and spatial attention modules, and external attention modules. Firstly, the study feeds the input data through multiple parallel branches of the backbone network to extract features at different levels from the water sound signals. Secondly, it employs the channel and spatial attention modules to weight the channels and spatial dimensions of the water sound signals. Finally, the external attention module integrates external memory units and additional computations to guide feature extraction and prediction, significantly improving the recognition rate and robustness of the model. Experimental results demonstrate that the proposed MEANet achieves a recognition rate of 98.84% on the ShipsEar dataset, outperforming other comparative algorithms.