We have established a simple process that allows for the one-step synthesis of KxFe2-ySe2 single crystals, which exhibit high critical current density Jc. The post annealing and quenching technique has improved the homogeneity of as-grown crystals, resulting in full shielding of the external magnetic field. The quenched crystals show a superconducting transition at Tconset = 32.9 K and Tczero = 32.1 K. The upper critical fields mu_{0}Hc2(0) for H//ab and H//c are estimated to be ~206 and ~50 T, respectively. The critical current densities Jc for H//ab and H//c reach as high as 1.0times10^{5} and 3.4times10^{4} A/cm2 at 5 K. Furthermore, Jc exhibits a high field performance and a significantly weak temperature dependence up to 5 T, suggesting strong pinning. These results demonstrate that KxFe2-ySe2 would be a promising candidate material for practical applications.