Drone object detection in low-altitude airspace plays an essential role in many practical applications, such as security and airspace monitoring. Despite the remarkable progress made by many methods, drone object detection still remains challenging due to the complex background and huge differences in scales of drones. To address the above issues, an improved fully convolutional one-stage object detection (FCOS) model based on adaptive weighted feature fusion (AWFF) module is proposed for multiscale drone object detection in complex background. By learning the spatial relevance of feature maps at each scale and improving the scale invariance of features based on the channel attention mechanism, AWFF module could adaptively fuse the features of adjacent scale. In addition, a receptive field enhancement module is designed to reduce the information loss in the feature fusion process. Extensive experiments are conducted to evaluate the effectiveness of the proposed module and method on the constructed low-altitude drone dataset, which concludes that the mean average precision of the AWFF-FCOS is increased by 2.1% compared with the baseline method. And extensive ablation experiments further demonstrate that the proposed AWFF module and REF module could be integrated into the state-of-the-art method to improve the performance of drone object detection.