Existing region-based object detectors are limited to regions with fixed box geometry to represent objects, even if those are highly non-rectangular. In this paper we introduce DP-FCN, a deep model for object detection which explicitly adapts to shapes of objects with deformable parts. Without additional annotations, it learns to focus on discriminative elements and to align them, and simultaneously brings more invariance for classification and geometric information to refine localization. DP-FCN is composed of three main modules: a Fully Convolutional Network to efficiently maintain spatial resolution, a deformable part-based RoI pooling layer to optimize positions of parts and build invariance, and a deformation-aware localization module explicitly exploiting displacements of parts to improve accuracy of bounding box regression. We experimentally validate our model and show significant gains. DP-FCN achieves state-of-the-art performances of 83.1% and 80.9% on PASCAL VOC 2007 and 2012 with VOC data only.