This paper addresses the challenge of representing high-fidelity volumetric videos with low storage cost. Some recent feature grid-based methods have shown superior performance of fast learning implicit neural representations from input 2D images. However, such explicit representations easily lead to large model sizes when modeling dynamic scenes. To solve this problem, our key idea is reducing the spatial and temporal redundancy of feature grids, which intrinsically exist due to the self-similarity of scenes. To this end, we propose a novel neural representation, named dynamic codebook, which first merges similar features for the model compression and then compensates for the potential decline in rendering quality by a set of dynamic codes. Experiments on the NHR and DyNeRF datasets demonstrate that the proposed approach achieves state-of-the-art rendering quality, while being able to achieve more storage efficiency. The source code is available at https://github.com/zju3dv/compact_vv.