Using the full-potential linearized augmented plane wave method, we studied the electronic energy band structures of β-pyrochlore superconductors AOs2O6（A=K, Rb, Cs）. The values of electronic density of states at the Fermi level have been significant enhanced for the three compounds due to taking to consideration of the spin-orbit coupling and the on-site Coulomb interactions. The electronic Coulomb correlation constants λc=1.55, 1.12 and 0.73 were obtained. Analyzing the electronic mass enhancement parameters obtained from the experimental data and the calculated electronic density of states, we deduced the electron-phonon coupling constants λep=1.56, 0.78 and 1.08 for the three compounds, respectively. It is suggested that KOs2O6 is a strongly-correlated and strongly electron-phonon coupled system, while RbOs2O6 and CsOs2O6 are medium in these properties.