Given the growing threat of Android malware, its family classification is important for identifying new variants, building robust signatures, assessing threat levels, and planning defenses. Since static and host-based dynamic classification techniques suffer from several limitations such as low adversarial capabilities, network-based dynamic techniques have been proposed as a complementary way. However, existing network-based approaches are heavily engineered on a specific application protocol (i.e., HTTP) and implement classification based on domain-expert driven features, rendering them hardly generalizable to many real-world classification scenarios (e.g., TLS encryption and unknown application protocols) and unable to keep pace with the rapid evolution of Android malware. To address these issues, we propose F2DC, a new Android malware classification method based on raw traffic and neural networks. F2DC characterizes Android malware from raw payload rather than application protocols and is therefore application-protocol independent and encryption-agnostic in principle. A novel traffic encoding scheme called F2D is designed to map the raw payload space into a flow-based latent feature space that facilitates convolutional neural networks (CNNs) to distill more discriminative features for effective classification. Experiments show that F2DC outperforms state-of-the-art methods and exhibits highly competitive performance against popular mobile antivirus (AV) tools. These results indicate that F2DC is a promising network-based Android malware classification solution complementary to existing alternatives.