This paper considers utilizing radar multipath returns to locate a non-line of sight (NLOS) target hidden behind an L-shaped corner. To handle this problem, we propose a novel NLOS target localization algorithm based on grid matching. First, a multipath propagation model based on the characters of the real data received by an L-band single-input single-output (SISO) ultra-wideband (UWB) radar is established. Then, a novel NLOS target localization algorithm based on times of arrival (TOAs) of round-trip multipath returns to construct the grid matching matrix is proposed. The principle of this algorithm is to calculate the TOAs of each grid based on the multipath propagation model, and then find the grid that is closest to the measured TOAs. This method can cope with the case while some missing multipaths happen. Simulation and experimental results validate the proposed algorithm.