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The multicast technology implements a very high-efficiency point-to-multipoint data transmission over IP networks (IPv4 and IPv6). Multicast protocols reduces network load, eliminates traffic redundancy, and saves network bandwidth. Therefore, widely used in WAN applications as online games, video conferencing and IPTV. This research focuses on IP multicast routing problem called center selection problem of shared tree with the best root classified as NP-complete type tested in IPv6 multicast network. The current research aims to improve select the best location of the RP for PIM-SMv6 protocol through propose a compound solution for multicast RP selection problem. The proposed algorithm called Greedy based RP selection algorithm (GRPSA), designed to select the best RP for PIM-SMv6 multicast routing protocol based on fitness criteria supported by Dijkstra algorithm. Moreover, the development of GRPSA divided into two stages. The First, MATLAB deployed to implement our proposed algorithm (GRPSA) to select the best RP. The second stage uses GNS3 emulator to investigate the performance GRPSA compared to the other randomly nominated RPs in IPv6 multicast network.