Due to the limited storage and computing power, edge devices at the network edge cannot train deep learning models locally. Traditional deep learning training requires users to upload a local dataset to a cloud center, and trains the data using massive computation resources of the cloud center. However, it results in two bad effects: uploading a local dataset to a centralized cloud center controlled by a third party leaves user data privacy at risk; and uploading multimedia data will consume huge bandwidth resources of mobile users and storage resources of the cloud center, resulting in low scalability in term of the number of edge devices. To deal with these two problems, we propose an edge-enabled distributed deep learning platform by dividing a general deep learning training network into a front and back subnetwork. Specifically, the front subnetwork consisting of several layers is deployed close to input data and is trained separately at each edge device using the local dataset, and the outputs of all front subnetworks are sent to the back subnetwork for later training at a cloud center; while the back subnetwork is deployed at the cloud center, and its output is sent to each front subnetwork. As no original dataset is transferred from edge devices to the cloud center, the platform can protect data privacy and has high scalability. Above that, another two measures are taken to ensure data privacy: asymmetric encryption technology is adopted to guarantee the safety and integrality of the transferred parameters between edge servers and the cloud center; and blockchain technology is used to monitor the actions of the stakeholders in this platform and thereby ensure trust among the stakeholders. Experimental results show the validation of the proposed method.