Quasi-free α-α knock-out collisions in Be9 are investigated by using the α-particle model, in order to test further the validity of the α-cluster picture in Be9 and to clarify the reaction mechanism in terms of well-established α-α and n-α potentials. The α-particle model wave function of Be9 is constructed on the basis of the above potentials and the exclusion principle procedure. Quasi-free α-α scattering is treated in the impulse approximation. Off-the-energy shell effects are completely calculated. The effects of the broad resonant state of He5 are also taken into account in terms of the final state n-α interaction. These features and the admixture of the excited states of the Be8-core determine the angular correlation of the reaction products. The theory succeeds in explaining satisfactorily both the shape and the magnitude of the experimental angular correlation distribution at incident energies 30 ∼ 40 MeV. It is suggested that the experimental data at about 23 MeV are of particular interest. It is noted that these results are derived only from the actual nuclear forces and do not involve any free parameters.