Preference-based Reinforcement Learning (PbRL) provides a way to learn high-performance policies in environments where the reward signal is hard to specify, avoiding heuristic and time-consuming reward design. However, PbRL can suffer from slow convergence speed since it requires training in a reward model. Prior work has proposed learning a reward model from demonstrations and fine-tuning it using preferences. However, when the model is a neural network, using different loss functions for pre-training and fine-tuning can pose challenges to reliable optimization. In this paper, we propose a method to effectively leverage prior knowledge with a Residual Reward Model (RRM). An RRM assumes that the true reward of the environment can be split into a sum of two parts: a prior reward and a learned reward. The prior reward is a term available before training, for example, a user's ``best guess'' reward function, or a reward function learned from inverse reinforcement learning (IRL), and the learned reward is trained with preferences. We introduce state-based and image-based versions of RRM and evaluate them on several tasks in the Meta-World environment suite. Experimental results show that our method substantially improves the performance of a common PbRL method. Our method achieves performance improvements for a variety of different types of prior rewards, including proxy rewards, a reward obtained from IRL, and even a negated version of the proxy reward. We also conduct experiments with a Franka Panda to show that our method leads to superior performance on a real robot. It significantly accelerates policy learning for different tasks, achieving success in fewer steps than the baseline. The videos are presented at https://sunlighted.github.io/RRM-web/.