GaN-based micro-size light-emitting diode (mu LED) have emerged as a promising light sources for a wide range of applications in displays, visible light communication etc. In parallel with the two key technological bottlenecks: full-color scheme and mass transfer technique that need overcoming, it is known that the low external quantum efficiency (EQE) is also another challenge for mu LEDs from the perspective of manufacturing technology and device physics. The low EQE for GaN based mu LEDs is opposite to the common belief for GaN-based LEDs, such that GaN based LEDs are featured with high quantum efficiency, mechanically robust and energy saving. Therefore, in this work, we have reviewed the origin for the low EQE for mu LEDs. More importantly, we have also reported the underlying devices physics and proposed optimization strategies to boost the EQE for mu LEDs. Our work is targeted to provide a guideline for the community to develop high-performance GaN-based mu LEDs.