Non-line-of-sight (NLOS) imaging provides a fascinating way to see through obstacles. As one of the dominating NLOS imaging approaches, transient NLOS imaging uses ultrafast illumination and detection to sense hidden objects. Because ultrafast array detectors still face challenges in manufacture or cost, most existing transient NLOS imaging schemes use a point detector and therefore need a point-by-point scanning (PPS) process, rendering a relative low detection efficiency and long imaging time. In this work, we apply a passive mode single-pixel camera to implement spatial multiplexing detection (SMD) in NLOS imaging and achieve a higher efficiency of data acquisition. We analyze and demonstrate the superiority of SMD through both simulation and experiment. We also demonstrate a SMD scheme with compressed sensing (CS) strategy. A compression ratio as low as 18% is achieved. By utilizing SMD, we accomplish a boost of detection efficiency of up to 5 times compared with the traditional PPS mode. We believe that this SMD modality is certainly an important approach to prompt the development of NLOS imaging technologies.