In this paper, we first propose a new FPGA routing method in which seversal netw are routed concurrently by applying the readitional maze routing method. We then introduce CMRF (concurrent maze Router for FPGA) which can be used for the routing of FpGAs of symmetrical array type by applying our new routing method. Given a set of nets, the proposed routing method performas the maze propagation and backtracing independently for each net and determines the routing paths concurrently by competition among nets. In CMRF, using this routing method, q nets are selected from the nets to be routed and they are routed concurrently, where q is the user given parameter determined by considering the computing environment. This process is repeated until either all the nets are routed or the remaining unrouted nets fail to their maze propagations. The routing of these nets are completed using the rip-up and rerouting technique. We apply our routing method to ten randomly generated test examples in order to check its routing performance. The results show taht as we increase the value of q, the routing completion rate increases for all the examples. Note that when q=1, our method is similar to the conventinal maze routing method. We also compare CMRF with the CGE method which has been proposed by Brown et.al. For the five benchmark examples, CMRF complete the routing with less wire segments in each connection block than the wire segments needed in the CGE method of 100% routing.