microRNAs (miRNAs) are small non-coding RNAs which modulate the stability of gene targets and their rates of translation into proteins at transcriptional level and post-transcriptional level. miRNA dysfunctions can lead to human diseases because of dysregulation of their targets. Correct miRNA target prediction will lead to better understanding of the mechanisms of human diseases and provide hints on curing them. In recent years, computational miRNA target prediction methods have been proposed according to the interaction rules between miRNAs and targets. However, these methods suffer from high false positive rates due to the complicated relationship between miRNAs and their targets. The rapidly growing number of experimentally validated miRNA targets enables predicting miRNA targets with high precision via accurate data analysis. Taking advantage of these known miRNA targets, a novel recommendation system model (miRTMC) for miRNA target prediction is established using a new matrix completion algorithm. In miRTMC, a heterogeneous network is constructed by integrating the miRNA similarity network, the gene similarity network, and the miRNA-gene interaction network. Our assumption is that the latent factors determining whether a gene is the target of miRNA or not are highly correlated, i.e., the adjacency matrix of the heterogeneous network is low-rank, which is then completed by using a nuclear norm regularized linear least squares model under non-negative constraints. Alternating direction method of multipliers (ADMM) is adopted to numerically solve the matrix completion problem. Our results show that miRTMC outperforms the competing methods in terms of various evaluation metrics. Our software package is available at https://github.com/hjiangcsu/miRTMC.