Generating 3D dances from music is an emerged research task that benefits a lot of applications in vision and graphics. Previous works treat this task as sequence generation, however, it is challenging to render a music-aligned long-term sequence with high kinematic complexity and coherent movements. In this paper, we reformulate it by a two-stage process, i.e., a key pose generation and then an in-between parametric motion curve prediction, where the key poses are easier to be synchronized with the music beats and the parametric curves can be efficiently regressed to render fluent rhythm-aligned movements. We named the proposed method as DanceFormer, which includes two cascading kinematics-enhanced transformer-guided networks (called DanTrans) that tackle each stage, respectively. Furthermore, we propose a large-scale music conditioned 3D dance dataset, called PhantomDance, that is accurately labeled by experienced animators rather than reconstruction or motion capture. This dataset also encodes dances as key poses and parametric motion curves apart from pose sequences, thus benefiting the training of our DanceFormer. Extensive experiments demonstrate that the proposed method, even trained by existing datasets, can generate fluent, performative, and music-matched 3D dances that surpass previous works quantitatively and qualitatively. Moreover, the proposed DanceFormer, together with the PhantomDance dataset, are seamlessly compatible with industrial animation software, thus facilitating the adaptation for various downstream applications.