Deformable image registration is fundamental to longitudinal and population analysis. Geometric alignment of the infant brain MR images is challenging, owing to rapid changes in image appearance in association with brain development. In this paper, we propose an infant-dedicated deep registration network that uses the auto-context strategy to gradually refine the deformation fields to obtain highly accurate correspondences. Instead of training multiple registration networks, our method estimates the deformation fields by invoking a single network multiple times for iterative deformation refinement. The final deformation field is obtained by the incremental composition of the deformation fields. Experimental results in comparison with state-of-the-art registration methods indicate that our method achieves higher accuracy while at the same time preserves the smoothness of the deformation fields. Our implementation is available online.