Abstract: In a massively parallel processors（MPP） system, the router constitutes the primary factor influencing the performance of the interconnect network and MPP system. Through careful analysis of message routing on interconnection network, the concept of "the best network for routing"（BNR） is proposed. By using it a new BNR-based minimal deadlock-free fully-adaptive algorithm on mesh （BBFAM） is designed. With the new proposed dynamic-priority control technology and the freedom-degree based channel selection policy, a high performance router: BFR （the BNR-based fully adaptive router） is obtained.