Multispectral pedestrian detection has shown great advantages under poor illumination conditions, since the thermal modality provides complementary information for the color image. However, real multispectral data suffers from the position shift problem, i.e. the color-thermal image pairs are not strictly aligned, making one object has different positions in different modalities. In deep learning based methods, this problem makes it difficult to fuse the feature maps from both modalities and puzzles the CNN training. In this paper, we propose a novel Aligned Region CNN (AR-CNN) to handle the weakly aligned multispectral data in an end-to-end way. Firstly, we design a Region Feature Alignment (RFA) module to capture the position shift and adaptively align the region features of the two modalities. Secondly, we present a new multimodal fusion method, which performs feature re-weighting to select more reliable features and suppress the useless ones. Besides, we propose a novel RoI jitter strategy to improve the robustness to unexpected shift patterns of different devices and system settings. Finally, since our method depends on a new kind of labelling: bounding boxes that match each modality, we manually relabel the KAIST dataset by locating bounding boxes in both modalities and building their relationships, providing a new KAIST-Paired Annotation. Extensive experimental validations on existing datasets are performed, demonstrating the effectiveness and robustness of the proposed method. Code and data are available at: https://github.com/luzhang16/AR-CNN.