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In this paper, we propose an efficient timeslot allocation scheme to manage the network resource for a centralized indoor network under 60GHz millimeter-wave unlicensed spectrum. We develop a system model where both AP (access point) and devices are equipped with array antennas to improve the poor link budget in the 60GHz band. And the beamforming weighting vectors defined in the standard of IEEE 802.15.3c are employed in the system. Jain's fairness index in terms of the number of slots assigned to each device is adopted to ensure the fairness of the algorithm. Then, extensive simulations are conducted to demonstrate the accuracy of the analytical model and the efficiency of the proposed algorithm. The analysis and simulation results show that the proposed algorithm can always outperform the existing one at channel capacity, schedule length and fairness.