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Fog is a phenomenon that occurs very close to the ground or sea level, and when detected by satellite, it is difficult to distinguish it from the low-level cloud. Logistic regression can help identify the false detection of the low-level cloud as fog and improve the accuracy of fog detection. In this study, a Korean fog detection algorithm was developed by using a machine learning-based logistic regression model (LRM) at three time points throughout the day (daytime, nighttime, and dawn/dusk) according to the solar zenith angle. The visible reflectance (Ref) and infrared brightness temperature (BT) of Himawari-8, solar zenith angle, land/sea mask, digital elevation angle, clear-sky Ref, and clear-sky BT excluding cloud pixels, from 2017 to 2018, were used as training data. The model was constructed by selecting variables with high correlation with the target data through a stepwise elimination method among input data having independent relationships between variables. Cross-validation using test data (20% of training data) contributed to the optimization of LRM. The fog detection performance of LRM confirmed by cross-validation has a stability of 83%–94% with high accuracy. For quantitative validation in 2019 using a 3 × 3-pixel validation method, the average probability of detection (POD) in the spring was 0.89–0.92, while the false alarm rate (FAR) was 0.39–0.41; in autumn, the POD was 0.9–0.97 and FAR was 0.29–0.4. The sophistication of the threshold between fog and non-fog can affect the performance improvement of the model. Further evaluation of the fog detection accuracy confirmed the reliability of the fog probability based on the stepwise probability. Satellite images enabled quantitative comparisons and validation of the proposed method; the results indicate that the approach is stable, reliable, and accurate. LRM fog detection will contribute to the Korean fog detection forecast with high performance, while the machine learning method used to build LRM can improve the performance of other meteorological forecast systems.