  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 1.0\times10^{5} and 3.4\times10^{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.
