Neutron inelastic scattering studies have been performed on the quasi-two-dimensional spin-gap system CaV4O9. An energy gap of about 10 meV has been clearly observed in the magnetic excitation spectra at low temperatures. The Q-point of the minimum excitation energy may not correspond to the so-called (pi, pi), (pi, 0) or Gamma-points in the reciprocal cell of the two-dimensional tetragonal lattice. With decreasing temperature, the scattering intensity in the energy region around 12 meV begins to increase at about 100 K, which almost coincides with the temperature at which the susceptibility has a maximum value. This result may provide important information to understand the ''spin-gap anomaly'' of high-T-c oxides.