Visible light positioning (VLP) is widely believed to be a cost-effective answer to the growing demand for real-time indoor positioning. However, due to the high computational cost of image processing, most existing VLC-based systems fail to deliver satisfactory performance in terms of positioning speed and accuracy, both of which are crucial for the performance of indoor navigation. This paper proposes a novel VLP solution that provides accurate and high-speed indoor navigation via the designs of an elaborate flicker-free line coding scheme and a lightweight image processing algorithm. In addition, this solution has the advantage of supporting flicker mitigation and dimming, which are important for illumination. An Android-based system prototype has been developed for field tests on an off-the-shelf smartphone. Experimental results show that it supports indoor positioning for users moving at a speed of up to 18 km/h. In addition, it can achieve a high accuracy of 7.5 cm, and the computational time is reduced to 22.7 ms for single-luminaire and to 35.7 ms for dual-luminaries, respectively.