Visible light positioning (VLP) is a promising technology for indoor navigation. However, most studies of VLP systems nowadays only focus on positioning accuracy, whereas robustness and real-time ability are often overlooked, which are all indispensable in actual VLP situations. Thus, we propose a novel VLP method based on mean shift (MS) algorithm and unscented Kalman filter (UKF) using image sensors as the positioning terminal and a Light Emitting Diode (LED) as the transmitting terminal. The main part of our VLP method is the MS algorithm, realizing high positioning accuracy with good robustness. Besides, UKF equips the mean shift algorithm with the capacity to track high-speed targets and improves the positioning accuracy when the LED is shielded. Moreover, a LED-ID (the identification of the LED) recognition algorithm proposed in our previous work was utilized to locate the LED in the initial frame, which also initialized MS and UKF. Furthermore, experiments showed that the positioning accuracy of our VLP algorithm was 0.42 cm, and the average processing time per frame was 24.93 ms. Also, even when half of the LED was shielded, the accuracy was maintained at 1.41 cm. All these data demonstrate that our proposed algorithm has excellent accuracy, strong robustness, and good real-time ability.