The tropospheric delay is an important error source in the Global Positioning System (GPS) positioning and navigation applications. Although most of the tropospheric delays can be removed in the double-differencing (DD) positioning mode, their remaining residuals can still contaminate the positioning accuracy and become unpredictable when tropospheric condition encounters severe variations such as during a tropical cyclone (TC) event. We investigated the positioning performance of five baselines with lengths ranging from 7.8 to 49.9 km during the 2017 TC Hato. The results showed that the TC Hato brought a significant disturbance to the GPS baseline positioning results, particularly in the vertical (up) component. The TC Hato started to affect Hong Kong and the root mean squares (RMS) of GPS positioning errors increased dramatically from about 30 to 140 mm, when it was at a distance of 400–600 km from Hong Kong on August 22, 2017. We found that the vertical positioning errors on that day have the major periods: 2.7 h, 3.0 h, 3.4 h, 4.0 h, and 4.8 h. Examining the wet and hydrostatic parts of the tropospheric delays via the continuous wavelet spectral analysis, we found that the periodical variation of the positioning results on August 22 was caused by the periodical variation of the precipitable water vapor (PWV). The variation of differenced PWV between two baseline stations had consistent periods of 2–5 h. Besides, the periods of differenced PWV time series are in good agreement with the spiral rainband in the TC. This finding suggests that the TC Hato induce periodical PWV variations at two GPS stations of baseline, which resulted in GPS positioning errors of the same periods.