A burst of six pulses with an average power of 38.7 W are obtained for a pulse-burst picosecond 1064 nm laser system at 1 kHz. The six pulses have equal amplitudes and pulse spacings of 800 ps, the beam quality of the $M^2$ factor is less than 2, and the pulse width is 67 ps. Seed pulses are broadened from 22 to 136 ps by single-pass volume Bragg gratings. A laser-diode end-pump $\mathrm{Nd}\text{:}{\mathrm{YVO}}_4$ beam-splitting amplifier is used to divide and amplify a single pulse into six pulses. An Nd:YAG regenerative amplifier and a single-pass high-gain amplifier are applied.