Different size InGaN/GaN based micro-LEDs (μLEDs) are fabricated. An extremely high injection level above 16 kA/cm2 is achieved for 10 μm-diameter LED. The lateral current density and carrier distributions of the μLEDs are simulated by APSYS software. Streak camera time resolved photoluminescence (TRPL) results show clear evidence that the band-gap renormalization (BGR) effect is weakened by strain relaxation in smaller size μLEDs. BGR affects the relaxation of free carriers on the conduction band bottom in multiple quantum wells (MQWs), and then indirectly affects the recombination rate of carriers. An energy band model based on BGR effect is made to explain the high-injection-level phenomenon for μLEDs.