This paper introduces a novel representation of volumetric videos for real-time view synthesis of dynamic scenes. Recent advances in neural scene representations demonstrate their remarkable capability to model and render complex static scenes, but extending them to represent dynamic scenes is not straightforward due to their slow rendering speed or high storage cost. To solve this problem, our key idea is to represent the radiance field of each frame as a set of shallow MLP networks whose parameters are stored in 2D grids, called MLP maps, and dynamically predicted by a 2D CNN decoder shared by all frames. Representing 3D scenes with shallow MLPs significantly improves the rendering speed, while dynamically predicting MLP parameters with a shared 2D CNN instead of explicitly storing them leads to low storage cost. Experiments show that the proposed approach achieves state-of-the-art rendering quality on the NHR and ZJU-MoCap datasets, while being efficient for real-time rendering with a speed of 41.7 fps for 512 × 512 images on an RTX 3090 GPU. The code is available at https://zju3dv.github.io/mlp_maps/.