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To enhance the capacity of patients supported by wireless in-hospital monitoring systems, a bandwidth allocation scheme for the transmission of medical data in the wireless local area network (WLAN) is proposed. The problem of bandwidth allocation, subject to limited wireless bandwidth, quality of service (QoS) requirements of medical data transmission, as well as electromagnetic interference, is modeled as a non-polynomial (NP) optimization problem. To save the computation time of this NP problem, we propose an accelerated genetic algorithm by dynamically adjusting both the inheritance probability and the mutation probability, and then compare it with other off-the-shelf genetic algorithms. Our study shows that our proposed algorithm can save computation time and attain the same result of bandwidth allocation in comparison with other algorithms.