GPS has limitations in indoor applications. Consequently, other indoor localization techniques and systems are active areas of research. Visible Light Positioning (VLP) is a promising option, especially given the growing popularity of LED-based lighting and the expected adoption of the forthcoming Visible Light Communication (VLC). This paper reports a novel VLP technique. The developed technique uses received signal strength for ranging. It is followed by the iterative estimation of a location using spring relaxation. The performance of the proposed technique was experimentally evaluated in indoor settings and benchmarked against the lateration- and fingerprint-based localization approaches in multiple scenarios. The obtained results demonstrate that the proposed VLP approach offers an opportunity to outperform the existing techniques in terms of localization accuracy and precision.