A large number of studies have proved the importance of using microRNAs (miRNAs) as targets for small molecule (SM) drug therapy. But just exploring new SM-miRNA associations through experiments in biology is very expensive, so there are many current models to predict SM-miRNA associations, and most of the currently existed models have some drawbacks, in this paper, we use an adaptive bounded nuclear norm regularization model to predict SM-miRNA associations. Which constructs a heterogeneous SM-miRNA network using similarities and predicts associations by minimizing nuclear norms. It uses an adaptive algorithm for dynamic parameter adjustment and learning rate optimization, ensuring matrix elements are practical. The model introduces regularization to handle noise. Validation is done using two datasets and cross-validation methods. Based on dataset 1, the AUC (Area Under the Receiver Operating Characteristic Curve) values for global Leave-One-Out Cross-Validation (LOOCV), miRNA-fixed LOOCV, and 5-fold CV are 0.9815, 0.9779, and 0.9760, respectively. Furthermore, many predicted associations have been validated by experimental literature. All these results confirm that Our Model is a reliable tool for inferring potential SM-miRNA associations.