We experimentally demonstrate the amplification of picosecond pulses at high repetition rates through the coherent addition of successive pulses of a mode-locked pulse train in a high-finesse optical cavity equipped with cavity dumping. Amplification greater than 30 times is obtained at a repetition rate of 253 kHz, boosting the 5.3-nJ pulses from a commercial mode-locked picosecond Ti:sapphire laser to pulse energies of more than 150 nJ.