A clock monitor circuit includes a monitor and a tunable counter. The monitor can monitor a clock under test. The tunable counter can count an integer according to a reference clock and set a target number. If a stable signal relative to the clock under test is toggled, the tunable counter can switch the target number from a large number to a small number. The tunable counter can perform an automatic detection process, so as to transmit a check signal to the monitor. In response to the check signal, if the clock under test is undetectable, the monitor will not transmit any confirmation signal back to the tunable counter, and the tunable counter will gradually increase the integer. When the integer is equal to the target number, the tunable counter generates a failure signal.