Neural radiance fields (NeRF) have shown great success in modeling 3D scenes and synthesizing novel-view images. However, most previous NeRF methods take much time to optimize one single scene. Explicit data structures, e.g. voxel features, show great potential to accelerate the training process. However, voxel features face two big challenges to be applied to dynamic scenes, i.e. modeling temporal information and capturing different scales of point motions. We propose a radiance field framework by representing scenes with time-aware voxel features, named as TiNeuVox. A tiny coordinate deformation network is introduced to model coarse motion trajectories and temporal information is further enhanced in the radiance network. A multi-distance interpolation method is proposed and applied on voxel features to model both small and large motions. Our framework significantly accelerates the optimization of dynamic radiance fields while maintaining high rendering quality. Empirical evaluation is performed on both synthetic and real scenes. Our TiNeuVox completes training with only 8 minutes and 8-MB storage cost while showing similar or even better rendering performance than previous dynamic NeRF methods. Code is available at https://github.com/hustvl/TiNeuVox.