The climate of the $21^{st}$ century is likely to be significantly different from that of the 20th century because of human-induced climate change. An extreme weather event is defined as a climate phenomenon that has not been observed for the past 30 years and that may have occurred by climate change and climate variability. The abnormal climate change can induce natural disasters such as floods, droughts, typhoons, heavy snow, etc. How will the frequency and intensity of extreme weather events be affected by the global warming change in the $21^{st}$ century? This could be a quite interesting matter of concern to the hydrologists who will forecast the extreme weather events for preventing future natural disasters. In this study, we establish the extreme indices and analyze the trend of extreme weather events using extreme indices estimated from the observed data of 66 stations controlled by the Korea Meteorological Administration (KMA) in Korea. These analyses showed that spatially coherent and statistically significant changes in the extreme events of temperature and rainfall have occurred. Under the global climate change, Korea, unlike in the past, is now being affected by extreme weather events such as heavy rain and abnormal temperatures in addition to changes in climate phenomena.