The Lancang-Mekong River is an important international river in Southeastern Asia. In recent years, due to climate change, natural disasters, such as drought and flooding, have frequently occurred in the region, which has a negative effect on the sustainable development of the social economy. Due to the lack of meteorological monitoring data in the six countries across the region, the study of the characteristics of climate change in this area is still scarce. In this paper, we analyze the characteristics of climate change in the Lancang-Mekong sub-region (LMSR) during 2020–2100 based on the climatic data of CMIP5, using the linear trend rate method, cumulative anomaly method, the Mann–Kendall test, and Morlet wavelet analysis. The results showed that the annual mean temperature and annual precipitation in the LMSR increased significantly. The annual average temperature in this area increased at a rate of 0.219 °C/10a (p < 0.05) and 0.578 °C/10a (p < 0.05) in the RCP4.5 and RCP8.5 scenarios, respectively; the annual precipitation in the area was 29.474 mm/10a (p < 0.05) and 50.733 mm/10a (p < 0.05), respectively. The annual average temperature in the region changed abruptly from low to high temperatures in 2059 for the RCP4.5 scenario and 2063 for RCP8.5. The annual precipitation in the area changed from less to more in 2051 for the RCP4.5 scenario and 2057 for RCP8.5. The results of wavelet analysis showed that the annual mean temperature in the LMSR had no significant change period at the 95% confidence level under the scenario of RCP4.5 and RCP8.5. Under the scenario of RCP4.5 and RCP8.5, the annual precipitation had a significant 3.5-year and 2.5-year periodicity, respectively. Extreme climate events tended to increase against the background of global warming, especially in high emission scenarios.