The use of drones to observe ships is an effective means of maritime surveillance. However, the object scale from drone-captured images changes dramatically, presenting a significant challenge for ship detection. Additionally, the limited computing resources on drones make it difficult to achieve fast detection speed. To address these issues, we propose an efficient deep learning based network, namely the YOLOv5-ODConvNeXt, for ship detection from drone-captured images. YOLOv5-ODConvNeXt is a more accurate and faster network designed to improve the efficiency of maritime surveillance. Based on YOLOv5, we implement Omni-dimensional Convolution (ODConv) in the YOLOv5 backbone to boost the accuracy without increasing the network width and depth. We also replace the original C3 block with a ConvNeXt block in YOLOv5 backbone to accelerate detection speed with only a slight decline in accuracy. We test our model on a self-constructed ship detection dataset containing 3200 images captured by drones or with a drone view. The experimental results show that our model achieves 48.0% AP, exceeding the accuracy of YOLOv5s by 1.2% AP. The detection speed of our network is 8.3 ms per image on an NVIDIA RTX3090 GPU, exceeding the detection speed of YOLOv5s by 13.3%. Our code is available at https://github.com/chengshuxiao/YOLOv5-ODConvNeXt.