Digital orthodontics represents a prominent and critical application of computer vision technology in the medical field. So far, the labor-intensive process of collecting clinical data, particularly in acquiring paired 3D orthodontic teeth models, constitutes a crucial bottleneck for developing tooth arrangement neural networks. Although numerous general 3D shape generation methods have been proposed, most of them focus on single-object generation and are insufficient for generating anatomically structured teeth models, each comprising 24-32 segmented teeth. In this paper, we propose TeethGenerator, a novel two-stage framework designed to synthesize paired 3D teeth models pre- and post-orthodontic, aiming to facilitate the training of downstream tooth arrangement networks. Specifically, our approach consists of two key modules: (1) a teeth shape generation module that leverages a diffusion model to learn the distribution of morphological characteristics of teeth, enabling the generation of diverse post-orthodontic teeth models; and (2) a teeth style generation module that synthesizes corresponding pre-orthodontic teeth models by incorporating desired styles as conditional inputs. Extensive qualitative and quantitative experiments demonstrate that our synthetic dataset aligns closely with the distribution of real orthodontic data, and promotes tooth alignment performance significantly when combined with real data for training. The code and dataset are available at https://github.com/lcshhh/teeth_generator.