This paper investigates the prescribed-time (Pre-T) order-preserved (OP) consensus of multi-agent systems (MASs). First, we use a distinctive approach to define the neighbors of each agent based on the differences among agents in the index space. Then, based on a time-varying scaling function (TVSF), a Pre-T controller is proposed for each agent. By using the monotone system theory, it is demonstrated that the MAS in the index space can achieve the order-preserved consensus at any Pre-T with the proposed Pre-T controller, irrespective of each agent’s initial and control conditions. Finally, numerical examples are presented to demonstrate the effectiveness of our provided method.