Cancer is a disease that seriously threatens human life, and the study of cancer subtype classification has become the focus of current research. Gene expression profiles are an effective and widely used data in cancer research, but the sparse high-dimensional features lead to suboptimal results of classification methods. In this paper, we propose a deep learning method combining fully connected layer (FC layer) and convolutional neural network (CNN): FCDN to learn its key features from sparse high-dimensional data for cancer classification. Specifically, in the process of nonlinear dimensionality reduction, the key features are learned from the sparse global features, thereby overcoming the high-dimensional sparsity challenge. In the experiments, we compare the performance of FCDN with other four classification methods on high-dimensional datasets. The results show that the overall performance of FCDN is better than other methods, and it can obtain more ideal classification results.