Non-line-of-sight imaging technology is a new type of optical imaging technology, which is mainly used to detect hidden objects in corners. Aiming at the problem of slow speed data acquisition caused by complex imaging equipment and the need for scene scanning, a transmission imaging experimental device using nanosecond laser and APD array detector is proposed, which can achieve fast data acquisition without scene scanning. Compared with the previous system, the data acquisition time is greatly shortened. Aiming at the problem that the image reconstruction results are poor due to the data collected only at sparse angles or limited angles, maximize likelihood estimate maximization (MLEM) iterative algorithm is proposed for 3D image reconstruction of hidden objects. Experimental results show that: The MLEM iterative algorithm can well reconstruct the shape of the hidden object and effectively suppress the artifacts brought by the traditional back projection algorithm. Compared with the back projection algorithm, the structure similarity (SSIM) value of the hidden object at the depth of 150 cm was improved by 0.232 1, 0.387 8 and 0.438 9 in the third, sixth and tenth iterations, respectively. At the depth of 190 cm, the SSIM value of the results of three iterations (the 3rd, 6th and 10th iterations) increased by 0.314 6, 0.401 3 and 0.431 3, respectively. The results show that MLEM algorithm can greatly improve the reconstructed image quality.