We present Cross3DVG, a novel task for cross-dataset visual grounding in 3D scenes, revealing the limitations of existing 3D visual grounding models using restricted 3D resources and thus easily overfit to a specific 3D dataset. To facilitate Cross3DVG, we have created a large-scale 3D visual grounding dataset containing more than 63k diverse descriptions of 3D objects within 1,380 indoor RGB-D scans from 3RScan with human annotations, paired with the existing 52k descriptions on ScanRefer. We perform Cross3DVG by training a model on the source 3D visual grounding dataset and then evaluating it on the target dataset constructed in different ways (e.g., different sensors, 3D reconstruction methods, and language annotators) without using target labels. We conduct comprehensive experiments using established visual grounding models, as well as a CLIP-based 2D-3D integration method, designed to bridge the gaps between 3D datasets. By performing Cross3DVG tasks, we found that (i) cross-dataset 3D visual grounding has significantly lower performance than learning and evaluation with a single dataset, suggesting much room for improvement in cross-dataset generalization of 3D visual grounding, (ii) better detectors and transformer-based localization modules for 3D grounding are beneficial for enhancing 3D grounding performance and (iii) fusing 2D-3D data using CLIP demonstrates further performance improvements. Our Cross3DVG task will provide a benchmark for developing robust 3D visual grounding models capable of handling diverse 3D scenes while leveraging deep language understanding.