We report on the first, to the best of our knowledge, LED-pumped femtosecond regenerative amplifier. It is based on a Cr:LiSAF crystal pumped by 2240 blue LEDs via a Ce:YAG luminescent concentrator. The amplifier was seeded by pulses from a Ti:sapphire oscillator at 835 nm temporally stretched from 90 fs to 100 ps. At the output of the regenerative amplifier, we obtain 1 mJ pulse energy at a 10 Hz repetition rate, given by the frequency of the LED-pumping module. After compression, we obtain 100 fs pulses with a spectral bandwidth of 10 nm at 835 nm.