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Drought is a popular scientific issue in global climate change research. Accurate monitoring of drought has important implications for the sustainable development of regional agriculture in the context of increasingly complex global climate change. Deep learning is a widely used technique in the field of artificial intelligence. However, ongoing on drought monitoring using deep learning is relatively scarce. In this paper, the various hazard factors in drought development were comprehensively considered based on satellite data including Moderate Resolution Imaging Spectroradiometer (MODIS) and tropical rainfall measuring mission (TRMM) as multi-source remote sensing data. By using the deep learning technique, a comprehensive drought monitoring model was constructed and tested in Henan Province of China as an example. The results showed that the comprehensive drought model has good applicability in the monitoring of meteorological drought and agricultural drought. There was a significant positive correlation between the drought indicators of the model output and the comprehensive meteorological drought index (CI) measured at the site scale. The consistency rate of the drought grade of the two models was 85.6% and 79.8% for the training set and the test set, respectively. The correlation coefficient between the drought index of the model and the standard precipitation evapotranspiration index (SPED was between 0.772 and 0.910 (P < 0.01), which indicated a strong level of significance. The correlation coefficient between the drought index of the model and the soil relative moisture at a 10 cm depth was greater than 0.550 (P < 0.01), and there was a good correlation between them. This study provides a new method for the comprehensive assessment of regional drought.