The effects of macerals, ash, elemental analysis and moisture of wide range of Kentucky coal samples from calorific value of 23.65–34.68 MJ/kg (10,170–14,910 (BTU/lb)) on Hardgrove Grindability Index (HGI) have been investigated by multivariable regression method. Two sets of input: (a) macerals, ash and moisture (b) macerals, elemental analysis and moisture, were used for the estimation of HGI. The least square mathematical method shows that increase of the TiO₂ and Al₂O₃ contents in coal can decrease HGI. The higher Fe₂O₃ content in coal can result in higher HGI. With the increase of micrinite and exinite contents in coal, the HGI has been decreased and higher vitrinite content in coal results in higher HGI. The multivariable studies have shown that input set of macerals, elemental analysis and moisture in non-linear condition can be achieved an acceptable correlation, R = 90.38%, versus R = 87.34% for the input set of macerals, ash and moisture. It is predicted that elemental analysis of coal can be a better representative of mineral matters for the prediction of HGI than ash.