Vis-NIR　magneto-optical　crystals　are　the　key　materials　in　the　fields　of　optical　fiber　communication,　smart　grids,　optical　fiber　lasers,　and　so　on.　In　this　paper,　the　incongruent　melting　Tb3Al5O12　(TAG)　single　crystals　with　centimeter　size　and　high　quality　were　grown　rapidly　by　an　EFG　method　with　the　suitable　design　of　a　melt　component.　The　effects　of　the　sintering　temperature　of　polycrystalline　materials,　the　melt　component,　and　the　growth　rate　on　the　crystal　quality　were　discussed　in　detail.　The　Verdet　constants,　hardness,　thermal　expansion　coefficients,　specific　heat　capacities,　and　thermal　diffusivities　of　TAG　crystal　were　measured.　The　results　show　that　the　Verdet　constant　of　the　TAG　crystal　is　8-30%　larger　than　those　of　Tb3Sc2Al3O12　(TSAG)　and　Tb3Ga5O12　(TGG)　crystals.　Additionally,　the　TAG　crystal　also　has　the　advantage　in　both　thermal　conductivity　and　hardness.　Therefore,　the　TAG　crystal　has　good　comprehensive　performance　and　thus　has　important　application　prospects.