Fog computing is an extension of cloud computing that effectively alleviates the data congestion in the core network and reduces the computation latency and communication cost, which fully explores the computation and storage resources of devices at the edge of the network. The computation offloading in fog computing has created significant attention for improving the network energy efficiency and user experience. Existing deep learning-based computation offloading models have good adaptability to the networks and improve consumption of energy and service latency of computation tasks. However, these models do not consider the optimization allocation of network resources and fail to handle delay-sensitive and computation-intensive tasks efficiently. Thus, designing energy and delay co-aware computing offloading mechanisms with deep learning in fog computing networks is necessary for determining whether to offload computation tasks to the neighbor for the cloud to satisfy the requirements of delay-sensitive applications.