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We consider the resource allocation problem in a resource-constrained system for OFDMA-based relay networks. In the resource-constrained system, our allocation strategy is based on economic aim to maximize the user satisfaction which means we can get the more profits. It is impossible to meet all the users' data rate requirement in the resource-constrained system. So we divide the users into two classes: non realtime users and realtime users, and priority to satisfy the realtime users' requirement, because of the realtime users have a more stringent QoS requirement. Meanwhile a new user satisfaction model is formulated based on the different user classes. The numerical results show that our proposed resource allocation scheme can significantly improve the user satisfaction compared with a normal resource allocation scheme.