The phenomena of longitudinal mode quenching in a CuBr laser with two types of multiple-mirror compound resonators are reported. The multiple mode-locking pulse trains at a repetition rate equal to a multiple of the fundamental longitudinal mode spacing have been obtained. The highest repetition rate is up to 440 MHz. The experimental results indicate that the mulptiple mode-locking pulses at high and wide-range tunable repetition rate in CuBr laser can be generated by adjusting the structure parameters of the compound resonators, without shortening the length of the active medium.