Fog-computing network combines the cloud computing and fog access points (FAPs) equipped with mobile edge computing (MEC) servers together to support computation-intensive tasks for mobile users. However, as FAPs have limited computational capabilities and are solely assisted by a remote cloud center in the baseband processing unit (BBU) of the cloud radio access (C-RAN) network, the latency benefits of this fog-computing C-RAN network may be worn off when facing a large number of offloading requests. In this paper, we investigate the delay minimization problem for task offloading in a hierarchical fog-computing C-RAN network, which consists of three tiers of computational services: MEC server in radio units, MEC server in distributed units, and the cloud computing in central units. The receive beamforming vectors, task allocation, computing speed for offloaded tasks in each server and the transmission bandwidth split of fronthaul links are optimized by solving the formulated mixed integer programming problem. The simulation results validate the superiority of the proposed hierarchical fog-computing C-RAN network in terms of the delay performance.