FeTe0.8Se0.2 single crystals as-cast and post-annealed were prepared by the self-flux method. We have investigated the structural properties of samples by using the XRD, scanning electron microscope (SEM), energy dispersive X-ray (EDX), and magnetic techniques. The SEM results clearly demonstrate that Te ions are quite well substituted for Se ions in the FeSe lattice for the samples. From the XRD and EDX spectra of the both samples, it has been concluded that the post-annealing causes no change in the tetragonal structure of FeTe0.8Se0.2. According to M-H measurements, the perfect diamagnetism has been observed only in low field at 5 and 10 K temperatures. The trend of the magnetization versus temperature curves, measured under a magnetic field of 10 Oe, also support our conclusion about diamagnetic contribution in FeTe0.8Se0.2 single crystal explored in this study. The as-cast and post-annealed samples show the onset of diamagnetism at temperatures, T-c.on(mag), 12.45 and 13.27 K, respectively. In addition, those curves indicate that the high field value and some impurities reveal ferromagnetic interactions.