In this paper, we propose a transfer learning (TL)-enabled edge-CNN framework for 5G industrial edge networks with privacy-preserving characteristic. In particular, the edge server can use the existing image dataset to train the CNN in advance, which is further fine-tuned based on the limited datasets uploaded from the devices. With the aid of TL, the devices that are not participating in the training only need to fine-tune the trained edge-CNN model without training from scratch. Due to the energy budget of the devices and the limited communication bandwidth, a joint energy and latency problem is formulated, which is solved by decomposing the original problem into an uploading decision subproblem and a wireless bandwidth allocation subproblem. Experiments using ImageNet demonstrate that the proposed TL-enabled edge-CNN framework can achieve almost 85% prediction accuracy of the baseline by uploading only about 1% model parameters, for a compression ratio of 32 of the autoencoder.