This paper considers the non-line-of-sight (NLOS) vehicle localization problem by using millimeter-wave (MMW) automotive radar. Several preliminary attempts for NLOS vehicle detection are carried out and achieve good results. Firstly, an electromagnetic (EM) wave NLOS multipath propagation model for vehicle scene is established. Subsequently, with the help of available multipath echoes, a complete NLOS vehicle localization algorithm is proposed. Finally, simulation and experimental results validate the effectiveness of the established EM wave propagation model and the proposed NLOS vehicle localization algorithm.