A constant on-time pulse width control-based apparatus (103) capable of detecting a transient event of a voltage converter (100) includes a specific comparator (110), a logic circuit (115), and a controller (105). The specific comparator (110) generates a logic control signal to the logic circuit (115) according to two resultant signals (VC1, VC2) of the controller (105). The logic circuit (115) generates a pulse control signal (Ton) with an on-time pulse width to charge an output capacitor according to the logic control signal. The controller (105) generates the two resultant signals (VC1, VC2) to the specific comparator (110) by generating a voltage ramp signal (Vramp) and amplifying an output voltage ripple signal (Vripple) based on a reference voltage (Vref), and detects the transient event to dynamically adjust the on-time pulse width of the pulse control signal (Ton) according to the amplified output voltage ripple signal (VC1).