We have investigated excitonic quantum beats (QBs) at the mini-Brillouin-zone boundary (π-point) in a GaAs (6.8 nm)/AlAs (1.1 nm) superlattice by using a femtosecond reflection-type electro-optic sampling technique. Photoreflectance spectroscopy was adopted to characterize the optical transition energies of the heavy-hole (HH) and light-hole (LH) excitons at the mini-Brillouin-zone center (Γ-point) and the π-point. By systematically changing the pump-pulse energy in the energy region from the Γ-point exciton to the π-point exciton, we have succeeded to observe the QB of the HH and LH excitons at the π-point in addition to the ordinary QB at the Γ-point. The observed frequencies agree with the values estimated from the energy difference between the relevant two excitons. The decay time of the QB signal at the π-point is much shorter than that at the Γ-point. This behavior reflects a very fast relaxation process of the π-point excitons in the miniband dispersion.