The demand for encrypted communication is increasing with the continuous development of secure and trustworthy networks. In edge computing scenarios, the requirement for data processing security is becoming increasingly high. Therefore, the accurate identification of encrypted traffic has become a prerequisite to ensure edge intelligent device security. Currently, encrypted network traffic classification relies on single-feature extraction methods. These methods have simple feature extraction, making distinguishing encrypted network data flows and designing compelling manual features challenging. This leads to low accuracy in multi-classification tasks involving encrypted network traffic. This paper proposes a hybrid deep learning model for multi-classification tasks to address this issue based on the synergy of dilated convolution and gating unit mechanisms. The model comprises a Gated Dilated Convolution (GDC) module and a CA-LSTM module. The GDC module completes the spatial feature extraction of encrypted network traffic through dilated convolution and gating unit mechanisms. In contrast, the CA-LSTM module focuses on extracting temporal network traffic features. By employing a collaborative approach to extract spatio-temporal features, the model ensures feature extraction diversity, guarantees robustness, and effectively enhances the feature extraction rate. We evaluate our multi-classification model using the ISCX VPN-nonVPN public dataset. Experimental results show that the proposed method achieves an accuracy rate of over 95% and a recall rate of over 90%, significantly outperforming existing methods.