Support vector machines (SVM) and deep convolutional neural networks (DCNNs) are state-of-the-art classification techniques in many real-world applications. Our investigation aims at proposing a hybrid model combining DCNNs and SVM (called DCNN-SVM) to effectively predict very-high-dimensional gene expression data. The DCNN-SVM trains the DCNNs model to automatically extract features from microarray gene expression data and followed which the DCNN-SVM learns a non-linear SVM model to classify gene expression data. Numerical test results on 15 microarray datasets from Array Expression and Medical Database (Kent Ridge) show that our proposed DCNN-SVM is more accurate than the classical DCNNs algorithm, SVM, random forests.