Partial person re-identification (re-id) is a challenging problem, where only some partial observations (images) of persons are available for matching. However, few studies have offered a flexible solution of how to identify an arbitrary patch of a person image. In this paper, we propose a fast and accurate matching method to address this problem. The proposed method leverages Fully Convolutional Network (FCN) to generate certain-sized spatial feature maps such that pixel-level features are consistent. To match a pair of person images of different sizes, hence, a novel method called Deep Spatial feature Reconstruction (DSR) is further developed to avoid explicit alignment. Specifically, DSR exploits the reconstructing error from popular dictionary learning models to calculate the similarity between different spatial feature maps. In that way, we expect that the proposed FCN can decrease the similarity of coupled images from different persons and increase that of coupled images from the same person. Experimental results on two partial person datasets demonstrate the efficiency and effectiveness of the proposed method in comparison with several stateof-the-art partial person re-id approaches. Additionally, it achieves competitive results on a benchmark person dataset Market1501 with the Rank-1 accuracy being 83.58%.