The advancements of artificial intelligence models have demonstrated notable progress in the field of hydrological forecasting. However, predictions of extreme climate events are still a challenging task. This paper presents the development and verification procedures of a new hybrid intelligent model, namely convolutional long short-term memory (CNN-LSTM) for short-term meteorological drought forecasting. The CNN-LSTM conjugates the long short-term memory (LSTM) network with a convolutional neural network (CNN) as the feature extractor. The new model was implemented to forecast multi-temporal drought indices, three-month and six-month standardized precipitation evapotranspiration (SPEI-3 and SPEI-6), at two case study points located in Ankara province, Turkey. Statistical accuracy measures, graphical inspections, and comparison with benchmark models, including genetic programming, artificial neural networks, LSTM, and CNN, were considered to verify the efficiency of the proposed model. The results showed that the CNN-LSTM outperformed all the benchmarks. In quantitative visualization, it attained minimal root mean square error (RMSE = 0.75 and 0.43) for the SPEI-3 and SPEI-6 at Beypazari station and (RMSE = 0.73 and 0.53) for the SPEI-3 and SPEI-6 at Nallihan station over the testing periods. The proposed hybrid model was a promising and reliable modeling approach for the SPEI prediction and increased our knowledge about meteorological drought patterns.