The quasiparticle scattering interference phenomenon is studied in the presence of a single impurity within the renormalized Hubbard model. By calculation of the energy and momentum dependence of the Fourier transformed local density of states in the full Brillouin zone, the main features of the quasiparticle scattering interference phenomenon in cuprate superconductors can be described qualitatively by a single point-like impurity. In particular, it is shown that with increasing energy ,the position of the peak along the nodal ([0, 0] → [π, π]) direction moves steadily to large momentum region, while the position of the peak along the antinodal ([0, 0] → [π, 0]) moves towards to the center of Brillouin zone.