Millimeter-wave (mmWave) communication is an important technology to meet the demand of high data rate in sixth generation (6G) wireless networks. Blockage is a major obstacle to reliable transmissions for mmWave communication. In order to prevent complete blocking of concurrent multiple beams and measure the reliability of concurrent multi-beam transmissions, beam space isolation degree (BSID) and reliability coefficient are defined, based on which a joint multi-beam selection and transmission power allocation scheme that maximizes the tradeoff utility of instantaneous achievable rate and reliability. We break the original optimization problem into two subproblems (i.e., multi-beam selection subproblem and transmission power allocation subproblem) to reduce the computational complexity, and solve them iteratively until no further improvement of the system utility, where exact potential game is used to solve the former under fixed transmission power policy, and first-order Taylor expansion and Lagrangian multiplier algorithm are utilized to solve the latter under fixed concurrent multi-beam selection strategy. Evaluation results indicate that the proposed scheme provides better sum utility and sum reliability with lower complexity, which indicates that concurrent multi-beam transmissions can improve the reliability of mmWave communication.