Mineral　grain　size　heterogeneity　is　one　of　the　fundamental　reasons　leading　to　differences　in　rock　mechanical　behaviours.　Several　indices　have　been　proposed　to　quantify　grain　size　heterogeneity,　however,　the　applicability　of　the　existing　indices　is　limited　due　to　various　preconditions.　An　improved　grain　size　heterogeneity　index　H-e　was　proposed　in　this　study.　By　comparing　with　the　previous　index,　the　improved　index　was　proved　to　be　more　applicable　for　analysing　rock　mechanical　properties.　Through　a　series　of　grain-based　model　(GBM),　the　grain　size　heterogeneity　effect,　material　heterogeneity　effect　and　mineral　content　effect　were　further　discussed.　For　a　simple　grain　size　heterogeneity　effect,　the　crack　initiation　stress,　damage　stress,　peak　stress　and　crack　initiation　stress　ratio　of　rock　decreased　linearly　as　the　improved　index　H-e　increased.　After　accounting　for　the　material　heterogeneity　effect,　the　above　characteristic　stresses　and　elastic　modulus　decreased.　A　significant　material　heterogeneity　effect　and　mineral　content　effect　will　impact　the　linear　correlation　between　the　rock　macromechanical　parameters　and　the　H-e　index.　When　the　axial　stress　was　low,　the　grain　size　heterogeneity　had　little　effect　on　the　number　of　microcracks,　but　this　heterogeneity　became　the　main　factor　affecting　the　evolution　of　microcracks　as　the　axial　stress　increased.　The　number　of　intragrain　tensile　cracks　increases　and　the　number　of　intergrain　shear　cracks　decreases　with　increasing　H-e,　when　the　axial　stress　reached　the　rock　peak　strength.　Besides,　the　combined　effects　of　material　heterogeneity　and　mineral　content　may　control　the　type　and　number　of　microcracks,　further　weakening　the　effect　of　grain　size　heterogeneity.