In continual learning, networks confront a trade-off between stability and plasticity when trained on a sequence of tasks. To bolster plasticity without sacrificing stability, we propose a novel training algorithm called LRFR. This approach optimizes network parameters in the null space of the past tasks’ feature representation matrix to guarantee the stability. Concurrently, we judiciously select only a subset of neurons in each layer of the network while training individual tasks to learn the past tasks’ feature representation matrix in low-rank. This increases the null space dimension when designing network parameters for subsequent tasks, thereby enhancing the plasticity. Using CIFAR-100 and TinyImageNet as benchmark datasets for continual learning, the proposed approach consistently outperforms state-of-the-art methods.