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Due to the diverse sparsity, high dimensionality, and large temporal variation of dynamic point clouds, it remains a challenge to design an efficient point cloud compression method. We propose to code the geometry of a given point cloud by learning a neural volumetric field. Instead of representing the entire point cloud using a single overfit network, we divide the entire space into small cubes and represent each non-empty cube by a neural network and an input latent code. The network is shared among all the cubes in a single frame or multiple frames, to exploit the spatial and temporal redundancy. The neural field representation of the point cloud includes the network parameters and all the latent codes, which are generated by using back-propagation over the network parameters and its input. By considering the entropy of the network parameters and the latent codes as well as the distortion between the original and reconstructed cubes in the loss function, we derive a rate-distortion (R-D) optimal representation. Experimental results show that the proposed coding scheme achieves superior R-D performances compared to the octree-based G-PCC, especially when applied to multiple frames of a point cloud video. The code is available at https://github.com/huzi96/NVFPCC/.