MicroRNAs (miRNAs) have recently emerged as a new complex layer of gene regulation. MiRNAs act post-transcriptionally, influencing the stability, compartmentalization, and translation of their target mRNAs. Computational efforts to understand the post-transcriptional gene regulation by miRNAs have been focused on the target prediction tools, while quantitative kinetic models of gene regulation by miRNAs have so far largely been overlooked. We here develop a kinetic model of post-transcriptional gene regulation by miRNAs, focusing on the miRNAs' effect on increasing the target mRNAs degradation rates. The model is fitted to a temporal microarray dataset where human mRNAs are measured upon transfection with a specific miRNA (miRNA124a). The proposed model exhibits good fit with many target mRNA profiles, indicating that such type of models can be used for studying post-transcriptional gene regulation by miRNA. In particular, the proposed kinetic model can be used for quantifying the miRNA-mediated effects on its targets in the miRNA mis-expression experiments. The model makes an experimentally verifiable prediction of the miRNA124a decay rate, quantifies the miRNA-mediated effect on the target mRNAs degradation, and yields a good correspondence between the inferred and experimentally measured decay rates of human target mRNAs.