MicroRNAs (miRNAs) play a crucial role in various biological processes and human diseases, and are considered as therapeutic targets for small molecules (SMs). Due to the time-consuming and expensive biological experiments required to validate SM-miRNA associations, there is an urgent need to develop new computational models to predict novel SM-miRNA associations. The rapid development of end-to-end deep learning models and the introduction of ensemble learning ideas provide us with new solutions. Based on the idea of ensemble learning, we integrate graph neural networks (GNNs) and convolutional neural networks (CNNs) to propose a miRNA and small molecule association prediction model (GCNNMMA). Firstly, we use GNNs to effectively learn the molecular structure graph data of small molecule drugs, while using CNNs to learn the sequence data of miRNAs. Secondly, since the black-box effect of deep learning models makes them difficult to analyze and interpret, we introduce attention mechanisms to address this issue. Finally, the neural attention mechanism allows the CNNs model to learn the sequence data of miRNAs to determine the weight of sub-sequences in miRNAs, and then predict the association between miRNAs and small molecule drugs. To evaluate the effectiveness of GCNNMMA, we implement two different cross-validation (CV) methods based on two different datasets. Experimental results show that the cross-validation results of GCNNMMA on both datasets are better than those of other comparison models. In a case study, Fluorouracil was found to be associated with five different miRNAs in the top 10 predicted associations, and published experimental literature confirmed that Fluorouracil is a metabolic inhibitor used to treat liver cancer, breast cancer, and other tumors. Therefore, GCNNMMA is an effective tool for mining the relationship between small molecule drugs and miRNAs relevant to diseases.