Heavy-fermion metal Ce3Pd20Si6 exhibits an antiferroquadrupolar (AFQ) phase below TQ=0.5K and an antiferromagnetic (AFM) phase below TN=0.31K. The AFM phase can be suppressed by a very moderate magnetic field of only 0.7T. This places Ce3Pd20Si6 very close to a quantum critical point (QCP), which can be likely reached by a small hydrostatic or chemical pressure or by magnetic field. Such a proximity leads to non Fermi-liquid behavior and, in particular, to very high values of the electronic specific-heat coefficient, which reportedly can reach up to 8 J/(mol·K2) near the QCP, making Ce3Pd20Si6 one of the heaviest-electron systems known to date. To fully understand the complex phase diagram, further INS measurements are essential. Therefore, in this proposal, we suggest to map out the full 4D energy-momentum space of Ce3Pd20Si6, using cold-neutron time-of-flight spectrometer IN5 at ILL. In this experiment, we will observe the evolution of dispersive spin excitations with field, which can give us valuable clues to understanding the underlying physics of Ce3Pd20Si6.