The evergrowing diversity of encrypted and anonymous network traffic makes network management more formidable to manage the network traffic. An intelligent system is essential to analyse and identify network traffic accurately. Network management needs such techniques to improve the Quality of Service and ensure the flow of secure network traffic. However, due to the usage of non-standard ports and encryption of data payloads, the classical port-based and payload-based classification techniques fail to classify the secured network traffic. To solve the above-mentioned problems, this paper proposed an effective deep learning-based framework employed with flow-time-based features to predict heterogeneous secure network traffic best. The state-of-the-art machine learning strategies (C4.5, random forest, and K-nearest neighbour) are investigated for comparison. The proposed 1D-CNN model achieved higher accuracy in classifying the heterogeneous secure network traffic. In the next step, the proposed deep learning model characterises the major categories (virtual private network traffic, the onion router network traffic, and plain encrypted network traffic) into several application types. The experimental results show the effectiveness and feasibility of the proposed deep learning framework, which yields improved predictive power compared to the state-of-the-art machine learning techniques employed for secure network traffic analysis.