Recently, with the IPTV services, e-learning, real-time broadcasting and e-contents, many application services need the multicasting routing protocol. In this paper, the performance of the algorithm to assign the rendezvous router (RP: rendezvous point) in the center-based multicasting mesh network is analyzed. The estimated distance to select RP in the candidate nodes is calculated, and the node minimizing the distance is selected as the optimal RP. We estimate the distance by using the maximum distance, average distance, and mean of the maximum and average distance between the RP and members. The performance of the algorithm is compared with the optimal algorithm of all enumeration. With the assumptions of mesh network and randomly positioned for sources and members, the simulations for different parameters are studied. From the simulation results, the performance deviation between the algorithm with minimum cost and optimal method is evaluated as 6.2% average.