This paper aims to reconstruct an animatable human model from a video of very sparse camera views. Some recent works represent human geometry and appearance with neural radiance fields and utilize parametric human models to produce deformation fields for animation, which enables them to recover detailed 3D human models from videos. However, their reconstruction results tend to be noisy due to the lack of surface constraints on radiance fields. Moreover, as they generate the human appearance in 3D space, their rendering quality heavily depends on the accuracy of deformation fields. To solve these problems, we propose Animatable Neural Implicit Surface (AniSDF), which models the human geometry with a signed distance field and defers the appearance generation to the 2D image space with a 2D neural renderer. The signed distance field naturally regularizes the learned geometry, enabling the high-quality reconstruction of human bodies, which can be further used to improve the rendering speed. Moreover, the 2D neural renderer can be learned to compensate for geometric errors, making the rendering more robust to inaccurate deformations. Experiments on several datasets show that the proposed approach outperforms recent human reconstruction and synthesis methods by a large margin.