3D LiDAR place recognition plays a vital role in various robot applications' including robotic navigation, autonomous driving, and simultaneous localization and mapping. However, most previous studies evaluated their models on accumulated 2D scans instead of real-world 3D LiDAR scans with a larger number of points, which limits the application in real scenarios. To address this limitation, we propose a point transformer network with pyramid learnable tokens (PTNet-PLT) to learn global descriptors for an actual scanned 3D LiDAR place recognition. Specifically, we first present a novel shifted cube attention module that consists of a self-attention module for local feature extraction and a cross-attention module for regional feature aggregation. The self-attention module constrains attention computation on a locally partitioned cube and builds connections across cubes based on the shifted cube scheme. In addition, the cross-attention module introduces several learnable tokens to separately aggregate features of points with similar features but spatially distant into an arbitrarily shaped region, which enables the model to capture long-term dependencies of the points. Next, we build a pyramid architecture network to learn multi-scale features and involve a decreasing number of tokens at each layer to aggregate features over a larger region. Finally, we obtain the global descriptor by concatenating learned region tokens of all layers. Experiments on three datasets, including USyd Campus, Oxford Robot-Car, and KITTI, demonstrate the effectiveness and generalization of the proposed model for large-scale 3D LiDAR place recognition.