Distributed resource allocation is a fundamental problem in construction of distributed systems. Though a lot of distributed algorithms have been developed for the problem, many of them are only designed to satisfy the desired quality of the requested resources, without considering acceptable range of the quality of the requested resources. In this paper we propose a new distributed algorithm employing a concession method, by which a process can transfer a reserved resource to another process, so that more processes can use the resources in the same time, to increase the efficiency and still keep the satisfaction for the quality of the resources in an acceptable range. We redefine the problem, and give the design and implementation of the algorithm in the paper.