In this paper, a received signal strength assisted Perspective-three-Point positioning algorithm (R-P3P) is proposed for visible light positioning (VLP) systems. The basic idea of R-P3P is to joint visual and strength information to estimate the receiver position using 3 LEDs regardless of the LEDs' orientations. R-P3P first utilizes visual information captured by the camera to estimate the incidence angles of visible lights. Then, R-P3P calculates the candidate distances between the LEDs and the receiver based on the law of cosines and the Wu-Ritt's zero decomposition method. Based on the incidence angles, the candidate distances and the physical characteristics of the LEDs, R-P3P can select the exact distances from all the candidate distances. Finally, the linear least square (LLS) method is employed to estimate the position of the receiver. Due to the combination of visual and strength information of visible light signals, R-P3P can achieve high accuracy using 3 LEDs regardless of the LEDs' orientations. Simulation results show that R-P3P can achieve positioning accuracy within 10 cm over 70% indoor area with low complexity regardless of LEDs orientations.