This paper presents a concurrent channel time allocation scheme used in the reservation period for concurrent transmissions in 60-GHz wireless personal area networks (WPANs). To this end, the proposed resource allocation scheme includes an efficient method for creating a concurrent transmission group by using a table that indicates whether individual streams experience interference from other streams or not. The coordinator device calculates the number of streams that can be concurrently transmitted with each stream and groups them together on the basis of the calculation result. Then, the coordinator device allocates resources to each group such that the streams belonging to the same group can transmit data concurrently. Therefore, when the piconet coordinator (PNC) allocates the channel time to the individual groups, it should allow for maximizing the overall capacity. The performance evaluation result demonstrates that the proposed scheme outperforms the random grouping scheme in terms of the overall capacity when the beamwidth is $30^{circ}C$ and the radiation efficiency is 0.9.