This paper experimentally demonstrates that the AC impedance spectrum of the light-emitting diode (LED) as a photodetector heavily depends on the received optical power, which may cause the impedance mismatch between the LED and the post trans-impedance amplifier. The optical power dependent impedance of the LED is well fitted by a modified dispersive carrier transport model for inorganic semiconductors. The bandwidth of the LED-LED visible light communication link is further shown to decrease with the optical power received by the LED. This leads to a trade-off between link bandwidth and SNR, and consequently affects the choice of the proper data modulation scheme. The discovery of light-controllable AC impedance of LEDs and its preliminary theoretical model may shed new light on the study of simultaneous photoelectric and electro-optic responses of LEDs.