could also be used to detect broadband microwave photons. Based on the numerical simulations of the noise-driving phase dynamics of an underdamped Josephson junction, driven by the low-frequency triangular wave current, we argue that the microwave photons flowing across the JJ can be detected by probing the voltage switched signals of the JJ. Experimentally, we designed and fabricated the relevant Al/AlOx/Al Josephson device and measured its response to microwave photons at 50~mK temperature. Experimental results indicate that the weak microwave signals could be threatened as the additional noises modify the phase dynamics of the CBJJ, which could thus be detected by the generated JTD. The detection sensitivity is characterized by using the Kumar-Caroll index to differentiate the junction switched duration distributions, with and without microwave signal input. Although the demonstrated detection sensitivity is just −92~dBm (corresponding to approximately 30~photon/ns) for the microwave photons at ∼5GHz (which is manifestly deviated from the plasma frequency of the fabricated JJ), we argued, based on the relevant numerical simulations, that the generated JTD could be used to achieve the sensitive detection of the microwave photons at the plasma frequency of the JJ.