A high repetition rate, picosecond THz parametric amplifier (TPA) with a LiNbO3 (LN) crystal has been demonstrated in this work. At 10 kHz repetition rate, a peak power of 200 W and an average power of 12 {\mu}W have been obtained over a wide range around 2 THz; at 100 kHz repetition rate, a maximum peak power of 18 W and average power of 10.8 {\mu}W have been obtained. The parametric gain of the LN crystal was also investigated and a modified Schwarz-Maier model was introduced to interpret the experimental results.
