Deep neural networks on regular 1D lists (e.g., natural languages) and irregular 3D sets (e.g., point clouds) have made tremendous achievements. The key to natural language processing is to model words and their regular order dependency in texts. For point cloud understanding, the challenge is to understand the geometry via irregular point coordinates, in which point-feeding orders do not matter. However, there are a few kinds of data that exhibit both regular 1D list and irregular 3D set structures, such as proteins and non-coding RNAs. In this paper, we refer to them as 3D point lists and propose a Transformer-style PointListNet to model them. First, PointListNet employs non-parametric distance-based attention because we find sometimes it is the distance, instead of the feature or type, that mainly determines how much two points, e.g., amino acids, are correlated in the micro world. Second, different from the vanilla Transformer that directly performs a simple linear transformation on inputs to generate values and does not explicitly model relative relations, our PointListNet integrates the 1D order and 3D Euclidean displacements into values. We conduct experiments on protein fold classification and enzyme reaction classification. Experimental results show the effectiveness of the proposed PointListNet.