CdTe thin films were grown on indium tin oxide glass substrates by a closed-space sublimation method using a resistor heater. Crystalline structure, morphology, and band gaps of the films were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and optical absorption, respectively. The XRD analysis showed that the textures of the films were found to depend on the rate of increase in the heating current. The CdTe thin film had an (111) texture when the heating current rate was 2.0 A/min. The SEM analysis revealed that the film is composed of polyhedral grains of microns size. However, the (111) texture of the CdTe thin film observed by XRD decreased with the appearance of (220), (311), (400), (331), (422), and (511) peaks of the fcc CdTe phase when the heating current rate increased to 4.5 A/min. The (111) texture disappeared when the heating current was increased immediately from 0 A to the target current of 70 A. SEM results revealed that the grains in the film are round and the grain size is smaller than 1 μm. Optical absorption analysis showed that there is no distinctive difference in the band gaps of the films.