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Conventional training of a deep CNN based object detector demands a large number of bounding box annotations, which may be unavailable for rare categories. In this work we develop a few-shot object detector that can learn to detect novel objects from only a few annotated examples. Our proposed model leverages fully labeled base classes and quickly adapts to novel classes, using a meta feature learner and a reweighting module within a one-stage detection architecture. The feature learner extracts meta features that are generalizable to detect novel object classes, using training data from base classes with sufficient samples. The reweighting module transforms a few support examples from the novel classes to a global vector that indicates the importance or relevance of meta features for detecting the corresponding objects. These two modules, together with a detection prediction module, are trained end-to-end based on an episodic few-shot learning scheme and a carefully designed loss function. Through extensive experiments we demonstrate that our model outperforms well-established baselines by a large margin for few-shot object detection, on multiple datasets and settings. We also present analysis on various aspects of our proposed model, aiming to provide some inspiration for future few-shot detection works.