In digital dentistry, cone-beam computed tomography (CBCT) can provide complete 3D tooth models, yet suffers from a long concern of requiring excessive radiation dose and higher expense. Therefore, 3D tooth model reconstruction from 2D panoramic X-ray image is more cost-effective, and has attracted great interest in clinical applications. In this paper, we propose a novel dual-space framework, namely DTR-Net, to reconstruct 3D tooth model from 2D panoramic X-ray images in both image and geometric spaces. Specifically, in the image space, we apply a 2D-to-3D generative model to recover intensities of CBCT image, guided by a task-oriented tooth segmentation network in a collaborative training manner. Meanwhile, in the geometric space, we benefit from an implicit function network in the continuous space, learning using points to capture complicated tooth shapes with geometric properties. Experimental results demonstrate that our proposed DTR-Net achieves state-of-the-art performance both quantitatively and qualitatively in 3D tooth model reconstruction, indicating its potential application in dental practice.