The $p-CdIn_2$$Te_4$single crystal was grown in the three-stage vertical electric furnace by using Bridgman method. The quality of the grown crystal has been investigated by the x-ray diffraction and the photoluminescence measurements. From the photoluminescence spectra of the as-grown $CdIn_2$$Te_4$crystal and the various heat-treated crystals, the ($D^{circ}$, X) emission was found to be the dominant intensity in the photoluminescence spectrum of the $CdIn_2$T $e_4$:Cd, while the ($A^{circ}$, X) emission completely disappeared in the $CdIn_2$T $e_4$:Cd. However, the ($A^{circ}$, X) emission in the photoluminescence spectrum of the $CdIn_2$T $e_4$:Te was the dominant intensity like an as-grown $CdIn_2$T $e_4$crystal. These results indicated that the ($D^{circ}$, X) is associated with $V_{Te}$ acted as donor and that the ($A^{circ}$, X) emission is related to $V_{cd}$ acted as acceptor, respectively. The $p-CdIn_2$T $e_4$crystal was found to be obviously converted into the n-type after annealing in the Cd atmosphere. The origin of ( $D^{circ}$, $A^{circ}$) emission and its TO phonon replicas is related to the interaction between donors such as $V_{Te}$ or $Cd_{int}$, and accepters such as $V_{cd}$ or T $e_{int}$. Also, the In in the $CdIn_2$X$CdIn_4$was confirmed not to form the native defects because it existed in the stable form of bonds.