A significant challenge of visible-light communication systems (VLC) is to overcome their limited converge area in non-line-of-sight (NLOS) transmission. To tackle this problem, for the first time, a real-time high-speed dual-hop VLC system based on blue micro-light-emitting diodes (micro-LED) is proposed and experimentally demonstrated. Benefiting from the advantage of high electrical-to-optical (E-O) bandwidth of the micro-LED, the frequency-response measurements show that the 3-dB modulation bandwidth of 2 m free-space single-hop link is 880 MHz, and the dual-hop system can reach to 715 MHz over a 4 m communication distance. We then investigated the communication performance of our proposed single-hop and dual-hop systems. The real-time waveforms are analyzed at different positions of the dual-hop link and eye diagrams at the receiving terminal are captured for evaluation. Furthermore, the bit error rate (BER) at the target node is measured. The results demonstrate that a 1.1 Gbps on-off keying (OOK) signal with a BER less than the forward-error-correction (FEC) limit could be achieved over a 4 m NLOS free-space link. This work shows that the proposed dual-hop system based on a micro-LED can meet the requirements for most indoor NLOS-transmission scenarios.