Time-resolved two-photon photoemission (TR2PPE) from the Cu(100) surface is investigated by the Keldysh Green function method in order to analyze ultrafast dynamics of an electron wave packet in the image states of the surface. By numerical analysis, the quantum beats in the TR2PPE spectrum due to interference among the image states are reproduced, and the motion of the electron wave packet in front of the surface is demonstrated. It is discussed on the basis of the obtained results as to how the motion of the electron wave packet is evaluated from the TR2PPE spectrum.