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MicroRNAs (miRNAs) have significant implications in diverse human diseases and have proven to be effectively targeted by small molecules (SMs) for therapeutic interventions. However, current SM–miRNA association prediction models do not adequately capture SM/miRNA similarity. Matrix completion is an effective method for association prediction, but existing models use nuclear norm instead of rank function, which has some drawbacks. Therefore, we proposed a new approach for predicting SM–miRNA associations by utilizing the truncated schatten p-norm (TSPN). First, the SM/miRNA similarity was preprocessed by incorporating the Gaussian interaction profile kernel similarity method. This identified more SM/miRNA similarities and significantly improved the SM–miRNA prediction accuracy. Next, we constructed a heterogeneous SM–miRNA network by combining biological information from three matrices and represented the network with its adjacency matrix. Finally, we constructed the prediction model by minimizing the truncated schatten p-norm of this adjacency matrix and we developed an efficient iterative algorithmic framework to solve the model. In this framework, we also used a weighted singular value shrinkage algorithm to avoid the problem of excessive singular value shrinkage. The truncated schatten p-norm approximates the rank function more closely than the nuclear norm, so the predictions are more accurate. We performed four different cross-validation experiments on two separate datasets, and TSPN outperformed various most advanced methods. In addition, public literature confirms a large number of predictive associations of TSPN in four case studies. Therefore, TSPN is a reliable model for SM–miRNA association prediction.