High-resolution full-field optical coherence microscopy (FF-OCM) is demonstrated using a single broadband light-emitting diode (LED). The characteristics of the LED-illumination FF-OCM system are measured and compared to those obtained using a halogen lamp, the light source of reference in FF-OCM. Both light sources yield identical performance in terms of spatial resolution and detection sensitivity, using the same setup and camera. In particular, an axial resolution of 0.7 μm (in water) is reached. A Xenopus laevis tadpole and ex-vivo human skin have been imaged using both sources, resulting in similar images, showing for the first time that LEDs could favorably replace halogen lamps in high-resolution FF-OCM for biomedical imaging.