Studies have shown that microbes are closely related to human health. Clarifying the relationship between microbes and diseases that cause health problems can provide new solutions for the treatment, diagnosis, and prevention of diseases, and provide strong protection for human health. Currently, more and more similarity fusion methods are available to predict potential microbe-disease associations. However, existing methods have noise problems in the process of similarity fusion. To address this issue, we propose a method called MSIF-LNP that can efficiently and accurately identify potential connections between microbes and diseases, and thus clarify the relationship between microbes and human health. This method is based on matrix factorization denoising similarity fusion (MSIF) and bidirectional linear neighborhood propagation (LNP) techniques. First, we use non-linear iterative fusion to obtain a similarity network for microbes and diseases by fusing the initial microbe and disease similarities, and then reduce noise by using matrix factorization. Next, we use the initial microbe-disease association pairs as label information to perform linear neighborhood label propagation on the denoised similarity network of microbes and diseases. This enables us to obtain a score matrix for predicting microbe-disease relationships. We evaluate the predictive performance of MSIF-LNP and seven other advanced methods through 10-fold cross-validation, and the experimental results show that MSIF-LNP outperformed the other seven methods in terms of AUC. In addition, the analysis of Cystic fibrosis and Obesity cases further demonstrate the predictive ability of this method in practical applications.