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Yield prediction is of great significance for yield mapping, crop market planning, crop insurance, and harvest management. Remote sensing is becoming increasingly important in crop yield prediction. Based on remote sensing data, great progress has been made in this field by using machine learning, especially the Deep Learning (DL) method, including Convolutional Neural Network (CNN) or Long Short-Term Memory (LSTM). Recent experiments in this area suggested that CNN can explore more spatial features and LSTM has the ability to reveal phenological characteristics, which both play an important role in crop yield prediction. However, very few experiments combining these two models for crop yield prediction have been reported. In this paper, we propose a deep CNN-LSTM model for both end-of-season and in-season soybean yield prediction in CONUS at the county-level. The model was trained by crop growth variables and environment variables, which include weather data, MODIS Land Surface Temperature (LST) data, and MODIS Surface Reflectance (SR) data; historical soybean yield data were employed as labels. Based on the Google Earth Engine (GEE), all these training data were combined and transformed into histogram-based tensors for deep learning. The results of the experiment indicate that the prediction performance of the proposed CNN-LSTM model can outperform the pure CNN or LSTM model in both end-of-season and in-season. The proposed method shows great potential in improving the accuracy of yield prediction for other crops like corn, wheat, and potatoes at fine scales in the future.