In this work we propose a new pricing scheme for the wireless Internet services over WiMAX system. First, let us review the characteristics of wireless network which is based on multi-hop relay WiMAX system. Next, we show why usage-based and QoS-aware pricing scheme is needed in the wireless Internet. After that, we propose a theoretical model for the price of multimedia services called a DAP (DiffServ-aware pricing) scheme for the WiMAX multimedia network which takes into account the consumed radio resource of WiMAX system as well as the supported QoS in the IP backbone network. Finally, we present explicit formulae for the packet price, price of consumed radio resource, and price of consumed bytes.