In this paper, a received signal strength assisted perspective-three-point positioning algorithm (R-P3P) is proposed for visible light positioning (VLP) systems. Due to the directional propagation of visible light, the orientations of light-emitting diodes (LEDs) and receivers can affect the positioning accuracy seriously. To circumvent this challenge, R-P3P is proposed to mitigate the limitation on LEDs' and receiver's orientation in VLP systems. The basic idea of R-P3P is to jointly utilize visual and strength information to estimate the receiver position using 3 LEDs regardless of the orientations of LEDs and receivers. Simulation results show that R-P3P can achieve positioning accuracy within 10 cm over 70% of an indoor area with low complexity.