The electronic structure near the Fermi level (EF) of the beta-pyrochlore superconductor KOs2O6 is studied using laser-excited ultrahigh-resolution photoemission spectroscopy. The superconducting gap clearly opens across the superconducting transition (Tc=9.6 K), with the strong electron-phonon coupling value of 2Delta(0)/k B Tc>or=4.56. A fitting analysis identifies clear anomalies at Tp=7.5 K in the temperature dependencies of the superconducting gap size and the quasiparticle relaxation lifetime. These anomalies and the fine spectral structures arising from phonons suggest that the existence of the rattling behavior of K ions significantly affects the superconductivity in KOs2O6.