In this paper, we consider a positive consensus problem for some high-order linear multi-agent systems. Compared with existing consensus results, the most distinct feature of the formulated problem is that the state variables of all heterogeneous agents are confined to the positive orthant. To solve this problem, we first present some auxiliary multi-agent systems as positive local reference generators and then incorporate the reference generator into some applicable decentralized tracking controller for each agent. The proposed two different kinds of distributed algorithms are proven to solve the positive consensus problem fulfilling certain prescribed pattern for this multi-agent system under switching topology. A simulation example is finally given to illustrate the effectiveness of our design.