In severe non-line-of-sight environment, the three-dimensional localization methods face a major challenge due to the undetectable directed path and the unavailable arrival angles. In this paper, we proposed a novel three-dimensional localization scheme by exploiting the distance and departure angle of single-bounce path, which is capable in non-line-of-sight localization even with lacking information of spatial arrival angles. With the help of height information of the scattering plane, we study the three-dimensional spatial location relationship among the reference station, unknown node and scatterers and devise a new optimization algorithm which can apply in severe non-line-of-sight environment. Furthermore, the performance of the algorithm is studied by using root mean-square error analysis and Cramer-Rao lower bound. The simulation results show that the derived analytical results closely match the simulated results. The numerical results of cumulative distribution function in location error demonstrate that utilizing sufficient single-bounce path signals can yield to acceptable three-dimensional positioning accuracy in severe non-line-of-sight multipath environments.