While exisiting weighted fair scheduling schemes guarantee minimum service rates of a shared server (such as a computer or a communication channel), maximum rate control was generally enforced by employing policing mechanisms. The previous approaches use either a concatenation of rate controller and scheduler, or a policer in front of scheduler. The concatenation method uses two sets of queues and management aparartus, and thus incurs overhead. The other method allows bursty job requests that may violate maximum rate constraint. In this paper, we present a new weighted fair scheduling scheme, WF²Q-M, to simultaneously support maximum rate control and minimum service rate guarantee. WF²Q-M proposes the virtual clock adjustment method to enforce maximum rate control by distributing the excess bandwidths of maximum rate constrained sessions to other sessions without recalculating the virtual starting and finishing times of regular sessions. In terms of performance metrics, we prove that WF²Q-M is theoretically bounded by a fluid reference model. A procedural scheduling implementation of WF²Q-M is proposed and proof of correctness is given. Finally, we conduct extensive experiments to show the performance of WF²Q-M is just as we claim.