Timely, accurate, and repeatable crop mapping is vital for food security. Rice is one of the important food crops. Efficient and timely rice mapping would provide critical support for rice yield and production prediction as well as food security. The development of remote sensing (RS) satellite monitoring technology provides an opportunity for agricultural modernization applications and has become an important method to extract rice. This paper evaluated how a semantic segmentation model U-net that used time series Landsat images and Cropland Data Layer (CDL) performed when applied to extractions of paddy rice in Arkansas. Classifiers were trained based on time series images from 2017–2019, then were transferred to corresponding images in 2020 to obtain resultant maps. The extraction outputs were compared to those produced by Random Forest (RF). The results showed that U-net outperformed RF in most scenarios. The best scenario was when the time resolution of the data composite was fourteen day. The band combination including red band, near-infrared band, and Swir-1 band showed notably better performance than the six widely used bands for extracting rice. This study found a relatively high overall accuracy of 0.92 for extracting rice with training samples including five years from 2015 to 2019. Finally, we generated dynamic maps of rice in 2020. Rice could be identified in the heading stage (two months before maturing) with an overall accuracy of 0.86 on July 23. Accuracy gradually increased with the date of the mapping date. On September 17, overall accuracy was 0.92. There was a significant linear relationship (slope = 0.9, r2 = 0.75) between the mapped areas on July 23 and those from the statistical reports. Dynamic mapping is not only essential to assist farms and governments for growth monitoring and production assessment in the growing season, but also to support mitigation and disaster response strategies in the different growth stages of rice.