Massive multiple-input multiple-output (mMIMO) systems using sub-Terahertz (sub-THz) wave bands are viewed as a promising way to increase greatly the capacity of future mobile communications because they can provide a wider bandwidth than conventional wireless communications. Distributed mMIMO systems can improve the spatial multiplexing transmission performance by reducing spatial correlations among the MIMO channels in line-of-sight environments. Unfortunately, beam search is more complex than in conventional wireless communications, because each access point (AP) requires a very narrow beamwidth to compensate for the significant propagation attenuation in sub-THz waves and beam search must involve all distributed APs. To address this problem, this paper proposes a fast beam search method to limit the beam-sweep directions of beam sweep based on the beam combinations selected for the distributed APs in the past. Simulations show that the proposed method maintains the transmission capacity while greatly reducing the number of search beams compared to conventional all-AP exhaustive beam search. The results show based on 16 APs that while matching the transmission capacity attained by all-AP exhaustive or two-stage beam search methods, the proposed method reduces the number of search beams by APs (excluding the initial AP executed exhaustive beam search) by 90.8% at the 50th percentile and 62.5% at the 95th percentile compared to two-stage beam search for 50,000 sets of user equipment used for recording beam combinations before evaluating the performance.