We have reported the synthesis and characterization of FeTe0.6Se0.4 prepared by self-flux technique with two different cooling rates, namely 0.8 and 4.5(a similar to)C/h. The effect of cooling rate on the samples has been characterized by using scanning electron microscopy (SEM) together with energy dispersive X-ray (EDX) spectrometer, X-ray diffraction (XRD), magnetization and magnetic hysteresis techniques. Four strong peaks were observed in the powder XRD patterns of both samples corresponding to the reflected intensities from the (001), (002), (003), and (004) planes of the tetragonal structure having space group P4/nmm. However, sample 2 has extra peaks corresponding to various non-superconducting binary phases of FeSe and FeTe. It can be concluded that the multiphase behavior of system increases with increasing cooling rate. The critical current value at 5 K, J (c) (0), deduced from the M - H loops is approximately 5.6 x 10(4) A/cm(2) for sample 1 and 7.5 x 10(4) A/cm(2) for sample 2. Increasing in the critical current value can be attributed to non-superconducting binary phases acting as effective pinning centers in the system.