The effects of proximate and ultimate analysis, maceral content, and coal rank (R_max) for a wide range of Kentucky coal samples from calorific value of 4320 to 14960 (BTU/lb) (10.05 to 34.80 MJ/kg) on Hardgrove Grindability Index (HGI) have been investigated by multivariable regression and artificial neural network methods (ANN). The stepwise least square mathematical method shows that the relationship between (a) Moisture, ash, volatile matter, and total sulfur; (b) ln (total sulfur), hydrogen, ash, ln ((oxygen + nitrogen)/carbon) and moisture; (c) ln (exinite), semifusinite, micrinite, macrinite, resinite, and R_max input sets with HGI in linear condition can achieve the correlation coefficients (R²) of 0.77, 0.75, and 0.81, respectively. The ANN, which adequately recognized the characteristics of the coal samples, can predict HGI with correlation coefficients of 0.89, 0.89 and 0.95 respectively in testing process. It was determined that ln (exinite), semifusinite, micrinite, macrinite, resinite, and R_max can be used as the best predictor for the estimation of HGI on multivariable regression (R² = 0.81) and also artificial neural network methods (R² = 0.95). The ANN based prediction method, as used in this paper, can be further employed as a reliable and accurate method, in the hardgrove grindability index prediction.