Developing lifelong learning algorithms are mandatory for computational systems biology. Recently, many studies have shown how to extract biologically relevant information from high-dimensional data to understand the complexity of cancer by taking the benefit of deep learning (DL). Unfortunately, new cancer growing up into the hundred types that make systems difficult to classify them efficiently. In contrast, the current state-of-the-art continual learning (CL) methods are not designed for the dynamic characteristics of high-dimensional data. And data security and privacy are some of the main issues in the biomedical field. This paper addresses three practical challenges for class-incremental learning (Class-IL) such as data privacy, high-dimensionality, and incremental learning problems. To solve this, we propose a novel continual learning approach, called Deep Generative Feature Replay (DGFR), for cancer classification tasks. DGFR consists of an incremental feature selection (IFS) and a scholar network (SN). IFS is used for selecting the most significant CpG sites from high-dimensional data. We investigate different dimensions to find an optimal number of selected CpG sites. SN employs a deep generative model for generating pseudo data without accessing past samples and a neural network classifier for predicting cancer types. We use a variational autoencoder (VAE), which has been successfully applied to this research field in previous works. All networks are sequentially trained on multiple tasks in the Class-IL setting. We evaluated the proposed method on the publicly available DNA methylation data. The experimental results show that the proposed DGFR achieves a significantly superior quality of cancer classification tasks with various state-of-the-art methods in terms of accuracy.