Solidification　grain　structure　has　significant　impacts　on　the　final　properties　of　laser　powder　bed　fusion　(L-PBF)　fabricated　parts.　Yet,　the　understanding　of　grain　evolution　process　remains　limited.　This　work　aims　to　construct　a　real-time　coupled　Lattice　Boltzmann　model-Cellular　Automaton　simulation,　to　shed　light　on　the　effect　of　energy　input　on　grain　structure.　Our　simulations　first　reproduce　diverse　grain　structures　observed　experimentally　under　different　energy　inputs.　Four　representative　types　of　grains:　slanted　columnar　grain,　V-shaped　grain,　vertical　columnar　grain　and　＂equiaxed＂　grain　are　observed　under　low　energy　input.　While　the　slanted　columnar　grains　and　V-shaped　grains　disappear,　and　the　vertical　columnar　grains　exhibit　different　distributions　and　sizes　under　high　energy　input.　Moreover,　our　model　further　confirms　that　the　grain　morphology　depends　on　the　location　of　the　fusion　boundary　and　the　shape　of　melt　pool.　As　the　energy　input　increases,　the　origin　of　grain　evolution　changes　from　the　slanted　columnar　grains　to　the　vertical　columnar　grains　during　the　overlapping　process　due　to　the　location　movement　of　the　fusion　boundary,　leading　to　differential　grain　evolutions　and　the　resultant　grain　structures.　And　melt　pools　with　edges　and　bottoms　perpendicular　to　each　other　are　more　likely　to　produce　a　stronger　texture　intensity.　Additionally,　based　on　the　comparison　between　3D　morphology　and　2D　cross-section　morphology　of　the　grain,　we　discover　that　some　grains　can　be　easily　misjudged　by　2D　experimental　observation.　We　expect　the　proposed　modeling　framework　to　be　a　powerful　tool　in　the　future　to　guide　process　parameters　for　site-specific　microstructure　of　L-PBF　fabricated　parts.