In this work, a new indoor visible light positioning algorithm is proposed based on support vector machines (SVM) and polynomial regression. Two different multipath environments of an empty room and a furnished room are considered. The algorithm starts by addressing the received power distance relation, considering polynomial regression models fitted to the specific areas of the room. In the second stage, an SVM is used to classify the best-fitted polynomial, which is used with nonlinear least squares to estimate the position of the receiver. The results show that, in an empty room, the positioning accuracy improvement for the positioning error, ?p of 2.5 cm are 36.1, 58.3, and 72.2 % for three different scenarios according to the regions' distribution in the room. For the furnished room, a positioning relative accuracy improvement of 214, 170, and 100 % is observed for ?p of 0.1, 0.2, and 0.3 m, respectively.