Multicast communication is an important service in wireless mesh networks (WMNs). It covers a broad range of applications, including data distribution, video conferencing, and distance learning. In this paper, we discuss the issue of bandwidth guaranteed multicast routing in multi-channel multi-radio WMNs. The problem of our concern is to construct a tree per multicast session such that the cost of the system, which is defined as the amount of total consumed bandwidth, is minimized. In order to solve the problem efficiently, we design Bandwidth Guaranteed Minimum Cost Tree construction (BGMCT) algorithm. Our algorithm yields cost-effective solutions as it exploits the wireless broadcast advantage (WBA) property of the wireless medium. In the proposed algorithm, we have developed two strategies for constructing minimum cost trees. Firstly, the number of the relay nodes in each tree is minimized. Secondly, the amount of overlapping between the shortest paths which connect different destinations of each session to its source node, is taken into account. The simulation results demonstrate that our algorithm outperforms existing solutions. Moreover, BGMCT provides near to optimal outcomes in a reasonable time.Keywords Wireless mesh networks · WMN · Multicast · Bandwidth guaranteed tree · Wireless broadcast advantage · WBA · Multi-channel multi-radio networks · MC-MR