Optical positioning techniques have inherent ad-vantages such as high precision, low power consuming and immunity to the electromagnetic interference. However, it is challenging to estimate the non-line-of-sight (NLOS) targets using current optical positioning methods. In this work, we propose an NLOS ultraviolet positioning method based on a simplified single-scattering channel model, which can obtain both the location and the pointing direction of the transmit-ter. Numerical results demonstrated that the proposed NLOS ultraviolet positioning method can achieve a positioning error less than 2 meters and an azimuth error less than 2 degrees by using two photon-counting receivers under typical transceiver geometries within 100 meters. Besides, we found that the positioning performance can be improved by increasing the gap between two receiving elevation angles.