Abstract：This letter investigates the challenge of channel estimation in a multiuser millimeter-wave (mmWave) time-division duplexing (TDD) system. In this system, the base station (BS) uses a multi-antenna uniform linear array (ULA), while each mobile user has a fluid antenna system (FAS). Accurate channel state information (CSI) plays a crucial role in the precise placement of antennas in FAS. To tackle this issue, we propose a low-sample-size sparse channel reconstruction (L3SCR) method, capitalizing on the sparse propagation paths of mmWave channels. Simulation results show that our method obtains precise CSI with minimal hardware switching and pilot overhead. As a result, the system sum-rate approaches the upper bound with perfect CSI. Index Terms: Channel estimation, fluid antenna system, mul tiple access, millimeter-wave communication.