Visible light positioning (VLP) is playing a critical role in delivering better location-based services. However, traditional VLP systems rely on line-of-sight (LOS) paths and have a requirement for large numbers of light-emitting diodes (LEDs) and sensors, making them unprepared for various scenarios. This paper proposes a three-dimensional (3D) non-line-of-sight (NLOS) VLP system using a single LED and an image sensor (IS) to address the problem of obstructed LOS paths. On the one hand, an optical camera communication (OCC) subsystem is designed to receive the transmitter’s position based on NLOS links. In contrast, two highlights are visible in the picture when the image sensor captures the reflected light from the floor. Using the proposed luminance distribution model (LDM), it can be demonstrated that the two highlights can be regarded as the projections formed by two virtual LEDs. Based on the projection equations of the two virtual LEDs, an image sensing algorithm can estimate the receiver’s position. Experimental results show that the proposed system can achieve a 90th percentile accuracy of < 22 cm for 3D positioning. To the best of author’s knowledge, this is the first work to demonstrate 3D NLOS VLP using just a single LED and an IS. Additionally, the proposed LDM is the first physically based model for the first reflected light to estimate the channel gain of a NLOS link.