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Predicting metastasis in early stages of cancer plays a crucial role in effectively controlling cancer progression and thereby improving patient survival outcomes. Although several computational methods have been developed to predict cancer metastasis, most focus on lymph node metastasis. Distant metastasis is more difficult to detect or predict than lymph node metastasis. In this study, we developed a multilayer perceptron (MLP) model to predict distant cancer metastases. We constructed a weighted gene interaction network and computed sample-specific differential gene correlations for individual cancer samples. The MLP model was trained on sample-specific differential gene correlations and tested on independent datasets of differential gene correlations from samples that were not used in training the model. The MLP model is capable of predicting whether or not distant metastasis will occur and potential distant metastatic sites. In independent testing, it predicted distant metastasis with a high performance (AUC of 0.95) and predicted metastatic sites with an average AUC of 0.97. In comparison of our model with other state-of-the-art methods using the same data set, our model showed better performance than the others. The prediction model developed in this study may help clinicians determine site-specific testing and treatment options.