This paper proposes an adaptive resource allocation for multi-tier computing systems to guarantee a fair QoS level under resource constraints of tiers. We introduce a multi-tier computing architecture which consists of a group of resource managers and an arbiter. Resource allocation of each client is managed by a dedicated resource manager. Each resource manager updates resources allocated to subtasks of its client by locally exchanging QoS levels with other resource managers. An arbiter compensates the updated resources to avoid overload conditions in tiers. Based on the compensation by the arbiter, the subtasks of each client are executed in corresponding tiers. We derive sufficient conditions for the proposed resource allocation to achieve a fair QoS level avoiding overload conditions in all tiers with some assumptions on a QoS function and a resource consumption function of each client. We conduct a simulation to demonstrate that the proposed resource allocation can adaptively achieve a fair QoS level without causing any overload condition.