We propose a novel continual learning method called Residual Continual Learning (ResCL). Our method can prevent the catastrophic forgetting phenomenon in sequential learning of multiple tasks, without any source task information except the original network. ResCL reparameterizes network parameters by linearly combining each layer of the original network and a fine-tuned network; therefore, the size of the network does not increase at all. To apply the proposed method to general convolutional neural networks, the effects of batch normalization layers are also considered. By utilizing residual-learning-like reparameterization and a special weight decay loss, the trade-off between source and target performance is effectively controlled. The proposed method exhibits state-of-the-art performance in various continual learning scenarios.