Iron-based superconductor FeSe _xTe _{1– x}has attracted attention because of its high upper critical field, low anisotropy, and high critical current density. Also, it is predicted to have nontrivial topological properties, so that it is a candidate of realizing Majorana fermion, when the superconductivity is combined with topological features. However, its flux pinning behavior and mechanism in superconducting state with varying Se/Te ratio have not been systematically studied . We use self-flux method to grow single crystal samples of FeSe _xTe _{1– x}with different xvalues (0.3, 0.4, 0.5 and 0.6). The structural and morphological properties of the monocrystalline samples are characterized by XRD and SEM. All samples show that they possess the expected crystalline structures and their lattice parameters vary with xvalue. The magnetic properties at low temperatures are also measured, showing that all samples have good superconductivity. Superconducting properties, such as critical current densities and flux pinning force densities, are extracted from the magnetic measurements and analyzed, and the flux pinning behavior is discussed. The best Se:Te ratio is determined to be nearly 0.4/0.6 based on the comparison among these properties of different samples. By utilizing the Dew-Hughes theory and analyzing the pinning force density peak, the flux pinning mechanism in the best samples ( x= 0.4, 0.5) can be regarded as the mixture of normal point pinning and Δ κ volume pinning. This work provides important information for the further study of the topological and superconducting properties of FeSe _xTe _{1– x}.