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Abstract In close‐range remote sensing data collected in a forest, occlusion often causes incomplete or sparse point cloud representations of individual trees, impeding accurate 3D reconstruction of tree architecture and estimation of tree height and volume. Recent developments in deep learning (DL) for 3D data have produced approaches for point cloud completion, which could potentially be applied to trees. We explored the potential of a DL approach to fill gaps in dense point clouds representing the main structures of deciduous trees by applying an existing transformer‐based completion model (PoinTr). Complete point clouds are required as training data, but even dense terrestrial laser scanning (TLS) data sets contain gaps caused by occlusion, making it nearly impossible to acquire such data. We therefore investigated the ability of point cloud completion models trained on a range of synthetic data sets to handle occlusion patterns in real‐world point clouds. Despite the limited data set, we successfully fine‐tuned a general pre‐trained completion model to fill gaps within 1 m3 segments of tree point clouds. Fine‐tuning on synthetic tree data improved the model's ability to complete tree objects compared with training on diverse artificial objects. However, the quality of the predictions was influenced by the level of sophistication of the synthetic data. Our results demonstrate that incorporating even limited real‐world TLS data during training can considerably improve completion results but may introduce additional noise in the predictions. 3D point cloud completion with DL has the potential to improve and fill gaps in point clouds of individual trees, facilitating further steps in the processing and analysis of 3D forest data.