This study was designed to detect and measure the concentration of radioactivity of natural radionuclides ($^{238}U$, $^{232}Th$, $^{40}K$) and artificial radionuclides ($^{137}Cs$, $^{60}Co$) present in the drinking water of the city of Busan and surrounding areas in South Korea, and also to measure the absorbed dose of radiation caused by these elements in the residents so as to help better manage the risk that these radionuclides pose in the future. For the purposes of the study, a total of 42 samples of water were collected from three key water sources (19 samples of groundwater, 4 samples of tap water, and 19 samples of surface water) and their contents were analyzed for radioactivity concentration. The results revealed that two natural radionuclides, $^{238}U$ and $^{232}Th$, exist in the groundwater with an average concentration of radioactivity of 3.34 Bq/L and $8.28{ imes}10^{-5}Bq/L$ respectively, while the surface water was found to contain the same two radionuclides with mean concentrations of 0.849 Bq/L and $1.103{ imes}10^{-4}Bq/L$ respectively. In addition, of the 19 samples of the groundwater, $^{137}Cs$ was found in eight of them and $^{60}Co$ was detected in ten. Of the four samples of the tap water, $^{137}Cs$ was detected in all samples and $^{60}Co$ was detected in three. Both $^{137}Cs$ and $^{60}Co$ were detected in all 12 samples of surface water. As far as $^{40}K$ is concerned, this element was detected in three of the 19 groundwater samples, but was not detected in any surface or tap water sample. In addition, the absorbed dose of $^{238}U$ from the groundwater was $7.94{ imes}10^{-8}Sv/y$, while the absorbed dose of $^{232}Th$ from the surface water was $9.33{ imes}10^{-13}Sv/y$. The absorbed dose of $^{137}Cs$ from the tap water was $7.33{ imes}10^{-5}Sv/y$, while the absorbed dose of $^{60}Co$ from the surface water was the highest at $4.23{ imes}10^{-6}Sv/y$.