A constant on-time pulse width control-based apparatus capable of detecting a transient event of a voltage converter includes a specific comparator, a logic circuit, and a controller. The specific comparator generates a logic control signal to the logic circuit according to two resultant signals of the controller. The logic circuit generates a pulse control signal with an on-time pulse width to charge an output capacitor according to the logic control signal. The controller generates the two resultant signals to the specific comparator by generating a voltage ramp signal and amplifying an output voltage ripple signal based on a reference voltage, and detects the transient event to dynamically adjust the on-time pulse width of the pulse control signal according to the amplified output voltage ripple signal.