DC magnetic measurements have been performed for beta-pyrochlore superconductor KOs2O6 (T-c = 9.6 K) under pressure for the precise determination of the pressure dependence of T-c, using a miniature diamond anvil cell combined with a commercial SQUID magnetometer. It is found that the critical temperature T-c shows a maximum of similar to 10 K at P=0.5 GPa. The maximum of T-c is higher than that for CsO2O6 and RbO2O6, in both of which T-c is known to increase and saturate at T-cm=8.8 K by the application of pressure, suggesting the enhanced superconductivity due to the rattling of K ions in an oversized cage of Os-O network. For the further application of pressure, T-c decreases linearly but the decreasing rate appears to be suddenly changed at P similar to 2 GPa and T-c similar to 8 K. The sharp bend of the T-c-P line probably corresponds to the transition concerning to the rattling motion which occurs at T-p=7.5 K at ambient pressure, suggesting the positive pressure dependence of T-p.