Fog computing is emerging as one promising solution to meet the increasing demand for ultra-low latency services in wireless networks. Taking a forward-looking perspective, we propose a Fog-Radio Access Network (F-RAN) model, which utilizes the existing infrastructure, e.g., small cells and macro base stations, to achieve the ultra-low latency by joint computing across multiple F-RAN nodes and near-range communications at the edge. We treat the low latency design as an optimization problem, which characterizes the tradeoff between communication and computing across multiple F-RAN nodes. Since this problem is N P-hard, we propose a latency-driven cooperative task computing algorithm with one-for-all concept for simultaneous selection of the F-RAN nodes to serve with proper heterogeneous resource allocation for multi-user services. Considering the limited heterogeneous resources shared among all users, we advocate the one-for-all strategy for every user taking others situation into consideration and seek for a winwin solution. The numerical results show that the low-latency services can be achieved by F-RAN via latency-driven cooperative task computing.