With the popularity of Android and its open source, the Android platform has become an attractive target for hackers, and the detection and classification of malware has become a research hotspot. Existing malware classification methods rely on complex manual operation or large-volume high-quality training data. However, malware data collected by security providers contains user privacy information, such as user identity and behavior habit information. The increasing concern for user privacy poses a challenge to the current malware classification scheme. Based on this problem, we propose a new android malware classification scheme based on Federated learning, named FedHGCDroid, which classifies malware on Android clients in a privacy-protected manner. Firstly, we use a convolutional neural network and graph neural network to design a novel multi-dimensional malware classification model HGCDroid, which can effectively extract malicious behavior features to classify the malware accurately. Secondly, we introduce an FL framework to enable distributed Android clients to collaboratively train a comprehensive Android malware classification model in a privacy-preserving way. Finally, to adapt to the non-IID distribution of malware on Android clients, we propose a contribution degree-based adaptive classifier training mechanism FedAdapt to improve the adaptability of the malware classifier based on Federated learning. Comprehensive experimental studies on the Androzoo dataset (under different non-IID data settings) show that the FedHGCDroid achieves more adaptability and higher accuracy than the other state-of-the-art methods.