Since the high transition temperature (High-Tc) superconductivity was discovered in the series of materials containing iron (Fe), their potential for the applications has been extensively scrutinized. In particular, a lot of effort has been made in achieving the high current-carrying ability by revealing the vortex pinning behavior. Here, we report on the critical current density (Jc) for the pristine Ba1-xKxFe2As2 single crystals with various K concentrations (0.25 ≤ x ≤ 0.52) determined by the magnetization hysteresis loop measurements. The x-dependence of Jc is characterized by a spike-like peak at x ~ 0.30, which corresponds to the under-doped region. This behavior is distinct from a moderate Tc dome with a broad maximum spanning from x ~ 0.3 to 0.5. For the under-doped samples, with increasing magnetic field (H), a second magnetization peak in Jc is observed, whereas for the optimally- and over-doped samples, Jc monotonically decreases with H. This result emphasizes that fine tuning of doping composition is important to obtain strong flux pinning. The origin of the characteristic doping dependence of Jc is discussed in connection with the orthorhombic phase domain boundary, as well as the chemical inhomogeneity introduced by the dopant substitutions.