A single geodetic GNSS station placed at the coast has the capability of a traditional tide gauge for sea-level measurements, with the additional advantage of simultaneously obtaining vertical land motions. The sea-level measurements are obtained using GNSS signals that have reflected off the water, using analysis of the signal-to-noise ratio (SNR) data. For the first time, we apply this technique to detect extreme weather-induced sea-level fluctuations, i.e., storm surges. We first derive 1-year sea-level measurements under normal weather conditions, for a GNSS station located in Hong Kong, and compare them with traditional tide-gauge data to validate its performance. Our results show that the RMS difference between the individual GNSS sea-level measurements and tide-gauge records is about 12.6 cm. Second, we focus on the two recent extreme events, Typhoon Hato of 2017 and Typhoon Mangkhut of 2018, that are ranked the third and second most powerful typhoons hitting Hong Kong since 1954 in terms of maximum sea level. We use GNSS SNR data from two coastal stations to produce sea-level measurements during the two typhoon events. Referenced to predicted astronomical tides, the storm surges caused by the two events are evident in the sea-level time series generated from the SNR data, and the results also agree with tidegauge records. Our results demonstrate that this technique has the potential to provide a new approach to monitor storm surges that complement existing tide-gauge networks.