This paper proposes a new control synthesis method for a class of discrete event systems modeled by controlled ordinary Petri nets with linear marking constraint. Monitor is constructed to track the system state resulted from the uncontrollable firing sequences. The maximally permissive feedback control policy then can be obtained based on the making of the monitor. No non-convex constraint transformation is introduced in the design procedure. The method is capable of synthesizing a class of net that cannot be treated using previous methods due to some necessary restrictions.