By means of growth unit of anion coordination polyhedron theory, growth units and equilibrium morphology of TiC Crystal which grew freely in titanium alloy were investigated. On the basis of the research on the characteristics of TiC crystal structure, energy level fission of orbit and bonding orbit of Ti crystal, through verifying the bonding energy released when TiC crystal formed different growth units, it can be concluded that the growth unit of TiC crystal which freely grew in molten titanium is TIC6. According to the stacking mode of the TiC6 crystal growth unit, the equilibrium morphology of TiC crystal is octahedron. However during the actual sample preparation, because of the undercooling and inhomogeneity of the solute distribution, TiC crystal may have different morphologies. Those conclusions are proved by the results of unidirectional solidification experiments in floating zone