Based on the 1965–2017 climate data of 18 meteorological stations in the Songliao Plain maize belt, the Coupled Model Intercomparision Project (CMIP5) data, and the 1998–2017 maize yield data, the drought change characteristics in the study area were analyzed by using the standardized precipitation evapotranspiration index (SPEI) and the Mann–Kendall mutation test; furthermore, the relationship between meteorological factors, drought index, and maize climate yield was determined. Finally, the maize climate yields under 1.5 °C and 2.0 °C global warming scenarios were predicted. The results revealed that: (1) from 1965 to 2017, the study area experienced increasing temperature, decreasing precipitation, and intensifying drought trends; (2) the yield of the study area showed a downward trend from 1998 to 2017. Furthermore, the climate yield was negatively correlated with temperature, positively correlated with precipitation, and positively correlated with SPEI-1 and SPEI-3; and (3) under the 1.5 °C and the 2.0 °C global warming scenarios, the temperature and the precipitation increased in the maize growing season. Furthermore, under the studied global warming scenarios, the yield changes predicted by multiple regression were −7.7% and −15.9%, respectively, and the yield changes predicted by one-variable regression were −12.2% and −21.8%, respectively.