We investigated the superconducting and transport properties in FeTe$_{1-x}$Se$_{x}$ (0.1 $leq$ $x$ $leq$ 0.4) single crystals prepared by O$_2$-annealing. Sharp superconducting transition width observed in magnetization measurement and the small residual resistivity prove the high quality of the crystals. All the crystals manifest large, homogeneous, and isotropic critical current density emph{J}$_c$ with self-field value over 10$^5$ A/cm$^2$ at 2 K. The large and field-robust critical current densities prove that the superconductivity in FeTe$_{1-x}$Se$_{x}$ (0.1 $leq$ $x$ $leq$ 0.4) is in bulk nature. The values of anisotropy parameter close to $T_c$ for crystals with different Se doping levels all reside in the range of 2 - 3. Hall coefficients $R_H$ keeps positive and almost constant value at high temperatures, followed by a sudden decreases before reaching $T$$_c$, which indicates that the electron-type charge carriers become dominant at low temperatures. Furthermore, the characteristic temperature for the sudden decrease in $R_H$ gradually increases with Se doping.
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