Over the years, numerous evidences have demonstrated that microbes living in the human body are closely related to human life activities and human diseases. However, traditional biological experiments are time-consuming and expensive, so it has become a research topic in bioinformatics to predict potential microbe-disease associations by adopting computational methods. In this study, a novel calculative method called BPNNHMDA is proposed to identify potential microbe-disease associations. In BPNNHMDA, a novel neural network model is first designed to infer potential microbe-disease associations, its input signal is a matrix of known microbe-disease associations, and its output signal is matrix of potential microbe-disease associations probabilities. And moreover, in the novel neural network model, a new activation function is designed to activate the hidden layer and the output layer based on the hyperbolic tangent function, and its initial connection weights are optimized by adopting Gaussian Interaction Profile kernel (GIP) similarity for microbes, which can improve the training speed of BPNNHMDA efficiently. Finally, in order to verify the performance of our prediction model, different frameworks such as the Leave-One-Out Cross Validation (LOOCV) and k-Fold Cross Validation ( k-Fold CV) are implemented on BPNNHMDA respectively. Simulation results illustrate that BPNNHMDA can achieve reliable AUCs of 0.9242, 0.9127 ± 0.0009 and 0.8955 ± 0.0018 in LOOCV, 5-Fold CV and 2-Fold CV separately, which are superior to previous state-of-the-art methods. Furthermore, case studies of inflammatory bowel disease (IBD), asthma and obesity demonstrate that BPNNHMDA has excellent prediction ability in practical applications as well.