Drones-aided ubiquitous applications play more and more important roles in our daily life. Accurate recognition of drones is required in aviation management due to their potential risks and even disasters. Radio frequency (RF) fingerprinting-based recognition technology based on deep learning is considered as one of the effective approaches to extract hidden abstract features from RF data of drones. Existing deep learning-based methods are either a high computational burden or low accuracy. In this paper, we propose a deep complex-valued convolutional neural network (DC-CNN) method based on RF fingerprinting for recognizing different drones. Compared with existing recognition methods, the DC-CNN method has the advantages of high recognition accuracy, fast running time and small network complexity. Nine algorithm models and two datasets are used to represent the superior performance of our system. Experimental results show that our proposed DC-CNN can achieve recognition accuracy of 99.5\% and 74.1\% respectively on 4 and 8 classes of RF drone datasets.