The side effects of drugs are not only harmful for human bodies but also the major causes of withdrawing approved drugs, which may bring great risks for pharmaceuticals companies. However, it is time-consuming and expensive to detect the side effects for a given drug via traditional experiments. In recent years, several computational methods have been proposed to predict the side effects of drugs. However, most methods cannot effectively integrate heterogeneous properties of drugs. In this study, we adopted a network embedding method, Mashup, to extract essential and informative drug features from several drug heterogeneous networks, representing different properties of drugs. For side effects, a network was also built, from which side effect features were extracted. These features can capture essential information of drugs and side effects in a network level. Drug and side effect features were combined together to represent each pair of drug and side effect, which was deemed as a sample in this study. And they were fed into a random forest (RF) algorithm to construct the prediction model, called RF network model. Several tests were performed on this model. The average of Matthews correlation coefficients (MCCs) on balanced and unbalanced datasets was 0.640 and 0.641, respectively. Such model was superior to the models incorporating other machine learning algorithms and one previous model. Finally, we also investigated the influence of two feature dimension parameters on the RF network model and found that our model was not very sensitive to these parameters.