Open-world 3D semantic occupancy prediction aims to generate a voxelized 3D representation from sensor inputs while recognizing both known and unknown objects. Transferring open-vocabulary knowledge from vision-language models (VLMs) offers a promising direction but remains challenging. However, methods based on VLM-derived 2D pseudo-labels with traditional supervision are limited by a predefined label space and lack general prediction capabilities. Direct alignment with pretrained image embeddings, on the other hand, often fails to achieve reliable performance because of inconsistent image and text representations in VLMs. To address these challenges, we propose AGO, a novel 3D occupancy prediction framework with adaptive grounding to handle diverse open-world scenarios. AGO first encodes surrounding images and class prompts into 3D and text embeddings, respectively, leveraging similarity-based grounding training with 3D pseudo-labels. Additionally, a modality adapter maps 3D embeddings into a space aligned with VLM-derived image embeddings, reducing modality gaps. Experiments on Occ3D-nuScenes show that AGO improves unknown object prediction in zero-shot and few-shot transfer while achieving state-of-the-art closed-world self-supervised performance, surpassing prior methods by 4.09 mIoU. Code is available at: https://github.com/EdwardLeeLPZ/AGO.