The dynamic variations of groundwater have been extensively studied, but there are few studies on the long-term time–frequency features of groundwater dynamic variations. Here we report the dynamic characteristics of the groundwater level and dissolved radon concentration based on the long-term (January 1988–March 2018) daily observation records and regional precipitation data in the Tengchong area, China. The results show that the precipitation (2–3 years and 13 years), groundwater level (13 years), and dissolved radon (9 years) all have multi-year periodic variations, which might be controlled by climate and solar radiation. The groundwater levels were highly correlated with rainfall amount, while the radon concentration variations were not only affected by rainfall but also by other complex factors. Furthermore, the changes of groundwater level and radon concentration lagged behind that of precipitation by about 3 months, and as the cycle range increased, the lag time tended to stabilize. During the observation period, the dissolved radon concentrations increased and decreased sharply. Radon concentration remained correlated with precipitation during the anomalous period. After the anomaly disappeared in 2002, however, its annual periodic characteristics weakened. The increase of radon concentrations may cause a potential risk for water utilization that requires more attention.