Non-line-of-sight (NLOS) imaging reveals hidden objects reflected from diffusing surfaces or behind scattering media. NLOS reconstruction is usually achieved by computational deconvolution of time-resolved transient data from a scanning single-photon avalanche diode (SPAD) detection system. However, using such a system requires a lengthy acquisition, impossible for capturing dynamic NLOS scenes. We propose to use a novel SPAD array and an optimization-based computational method to achieve NLOS reconstruction of 20 frames per second (fps). The imaging system's high efficiency drastically reduces the acquisition time for each frame. The forward projection optimization method robustly reconstructs NLOS scenes from low SNR data collected by the SPAD array. Experiments were conducted over a wide range of dynamic scenes in comparison with confocal and phase-field methods. Under the same exposure time, the proposed algorithm shows superior performances among state-of-the-art methods. To better analyze and validate our system, we also used simulated scenes to validate the advantages through quantitative benchmarks such as PSNR, SSIM and total variation analysis. Our system is anticipated to have the potential to achieve video-rate NLOS imaging.