With the advances in 5G and IoT devices, the industries are vastly adopting artificial intelligence (AI) techniques for improving classification and prediction-based services. However, the use of AI also raises concerns regarding data privacy and security that can be misused or leaked. Private AI was recently coined to address the data security issue by combining AI with encryption techniques but existing studies have shown that model inversion attacks can be used to reverse engineer the images from model parameters. In this regard, we propose a federated learning and encryption-based private (FLEP) AI framework that provides two-tier security for data and model parameters in an IIoT environment. We proposed a three-layer encryption method for data security and provided a hypothetical method to secure the model parameters. Experimental results show that the proposed method achieves better encryption quality at the expense of slightly increased execution time. We also highlighted several open issues and challenges regarding the FLEP AI framework's realization.