We consider the maximum throughput scheduling problem in a millimeter-wave wireless personal area network in which users can use adaptive modulation and coding schemes to change their data rates. The scheduling problem is to map transmissions to time slots so that the total throughput is maximized. Due to the ultra-wide bandwidth of the mm Wave band, bad scheduling tends to waste significant channel resource. It is worth the effort to consider a more sophisticated scheduling scheme than the simple serial TDMA scheme. The challenge is that the achieved data rate of one flow is limited by the interference from other transmissions in the same slot, which is unknown until the scheduling decision is known. We propose two scheduling algorithms for variable data rate transmissions. The first algorithm is a greedy algorithm, which always chooses the best option at the moment; the second one uses sorting to decide the order that flows are included in a slot. Both algorithms are interference-aware. The algorithms can be applied to transmissions with omnidirectional antennas as well as directional antennas. The simulation results show that the proposed algorithms achieve higher throughput than previous work for adaptive-rate scheduling.