A novel miniaturized Cr⁴⁺:YAG passively Q-switched Nd:YAG pulse-burst laser under 808 nm diode-laser pulse-pumping was demonstrated for the purpose of laser-induced plasma ignition, in which pulse-burst mode can realize both high repetition rate and high pulse energy simultaneously in a short period. Side-pumping configuration and two different types of laser cavities were employed. The pumping pulse width was constant at 250 μs. For the plane-plane cavity, the output beam profile was flat-top Gaussian and the measured M² value was 4.1 at the maximum incident pump energy of 600 mJ. The pulse-burst laser contained a maximum of 8 pulses, 7 pulses and 6 pulses for pulse-burst repetition rate of 10 Hz, 50 Hz and 100 Hz, respectively. The energy obtained was 15.5 mJ, 14.9 mJ and 13.9 mJ per pulse for pulse-burst repetition rate of 10 Hz, 50 Hz and 100 Hz, respectively. The maximum repetition rate of laser pulses in pulse-burst was 34.6 kHz for 8 pulses at the incident pump energy of 600 mJ and the single pulse width was 13.3 ns. The thermal lensing effect of Nd:YAG rod was investigated, and an plane-convex cavity was adopted to compensate the thermal lensing effect of Nd:YAG rod and improve the mode matching. For the plane-convex cavity, the output beam profile was quasi-Gaussian and the measured M2 value was 2.2 at the incident pump energy of 600 mJ. The output energy was 10.6 mJ per pulse for pulse-burst repetition rate of 100 Hz. The maximum repetition rate of laser pulses in pulse-burst was 27.4 kHz for 6 pulses at the incident pump energy of 600 mJ and the single pulse width was 14.2 ns. The experimental results showed that this pulse-burst laser can produce high repetition rate (>20 kHz) and high pulse energy (>10 mJ) simultaneously in a short period for both two different cavities.