Deep neural networks often severely forget previously learned knowledge when learning new knowledge. Various continual learning (CL) methods have been proposed to handle such a catastrophic forgetting issue from different perspectives and achieved substantial improvements. In this paper, a novel two-branch continual learning framework is proposed to further enhance most existing CL methods. Specifically, the main branch can be any existing CL model and the newly introduced side branch is a lightweight convolutional network. The output of each main branch block is modulated by the output of the corresponding side branch block. Such a simple two-branch model can then be easily implemented and learned with the vanilla optimization setting without whistles and bells. Extensive experiments with various settings on multiple image datasets show that the proposed framework yields consistent improvements over state-of-the-art methods.