Feature Pyramid Network (FPN) has been widely adopted to exploit multi-scale features for scale variation in object detection. However, intrinsic defects in most of the current methods with FPN make it difficult to adapt to the feature of different geometric objects. To address this issue, we introduce geometric prior into FPN to obtain more discriminative features. In this paper, we propose Geometry-aware Feature Pyramid Network (GaFPN), which mainly consists of the novel Geometry-aware Mapping Module and Geometry-aware Predictor Head.The Geometry-aware Mapping Module is proposed to make full use of all pyramid features to obtain better proposal features by the weight-generation subnetwork. The weights generation subnetwork generates fusion weight for each layer proposal features by using the geometric information of the proposal. The Geometry-aware Predictor Head introduces geometric prior into predictor head by the embedding generation network to strengthen feature representation for classification and regression. Our GaFPN can be easily extended to other two-stage object detectors with feature pyramid and applied to instance segmentation task. The proposed GaFPN significantly improves detection performance compared to baseline detectors with ResNet-50-FPN: +1.9, +2.0, +1.7, +1.3, +0.8 points Average Precision (AP) on Faster-RCNN, Cascade R-CNN, Dynamic R-CNN, SABL, and AugFPN respectively on MS COCO dataset.