A constant on-time pulse width control-based apparatus capable of detecting a transient event of a voltage converter, comprising: a specific comparator configured for generating a logic control signal (Sset) to a logic circuit according to two resultant signals (VC1, VC2) of a controller; the logic circuit, coupled to the specific comparator, configured for generating a pulse control signal (Ton) with an on-time pulse width to charge an output capacitor of an output stage circuit of the voltage converter according to the logic control signal; and the controller, coupled to the specific comparator and the logic circuit, configured for generating the two resultant signals (VC1, VC2) to the specific comparator by generating a voltage ramp signal (Vramp) and amplifying an output voltage ripple signal (Vripple) based on a reference voltage (Vref), and configured for detecting the transient event and adaptively adjusting the on-time pulse width of the pulse control signal (Ton) according to the amplified output voltage ripple signal; wherein the controller comprises: an error amplifier, coupled to an input of the specific comparator, configured for receiving the reference voltage (Vref) and an output voltage signal to generate and amplify the output voltage ripple signal (Vripple); and an estimation circuit, coupled to the output of the error amplifier, for detecting the transient event to adaptively adjust the on-time pulse width of the pulse control signal (Ton) according to the amplified output voltage ripple signal; wherein the estimation circuit comprises: a threshold voltage generator, configured for generating a specific threshold voltage (VCTH) for the amplified output voltage ripple signal; wherein the threshold voltage generator comprises: a resistor, a capacitor and a current source; and characterized in that the estimation circuit further comprises: a transconductance amplifier, coupled to the threshold voltage generator, configured for converting a voltage difference between the specific threshold voltage (VCTH) and the amplified output voltage ripple signal to generate a current signal for using the current signal as a source current or as a sink current for the logic circuit to dynamically extend or shorten the on-time pulse width of the pulse control signal (Ton) when the transient event is detected. a specific comparator configured for generating a logic control signal (Sset) to a logic circuit according to two resultant signals (VC1, VC2) of a controller; the logic circuit, coupled to the specific comparator, configured for generating a pulse control signal (Ton) with an on-time pulse width to charge an output capacitor of an output stage circuit of the voltage converter according to the logic control signal; and the controller, coupled to the specific comparator and the logic circuit, configured for generating the two resultant signals (VC1, VC2) to the specific comparator by generating a voltage ramp signal (Vramp) and amplifying an output voltage ripple signal (Vripple) based on a reference voltage (Vref), and configured for detecting the transient event and adaptively adjusting the on-time pulse width of the pulse control signal (Ton) according to the amplified output voltage ripple signal; an error amplifier, coupled to an input of the specific comparator, configured for receiving the reference voltage (Vref) and an output voltage signal to generate and amplify the output voltage ripple signal (Vripple); and an estimation circuit, coupled to the output of the error amplifier, for detecting the transient event to adaptively adjust the on-time pulse width of the pulse control signal (Ton) according to the amplified output voltage ripple signal; a threshold voltage generator, configured for generating a specific threshold voltage (VCTH) for the amplified output voltage ripple signal; wherein the threshold voltage generator comprises: a resistor, a capacitor and a current source; and a transconductance amplifier, coupled to the threshold voltage generator, configured for converting a voltage difference between the specific threshold voltage (VCTH) and the amplified output voltage ripple signal to generate a current signal for using the current signal as a source current or as a sink current for the logic circuit to dynamically extend or shorten the on-time pulse width of the pulse control signal (Ton) when the transient event is detected.