Inelastic neutron scattering measurements of a powder specimen of anion conducting superionic conductor CsPbCl3 were performed at 30, 100, 200 and 300 K by the time-of-flight (TOF) spectrometer. A low-lying dispersionless excitation near 1.8 meV was observed in the inelastic scattering spectra of CsPbCl3. The value of the low-energy excitation is almost independent of temperature. A low-lying dispersionless excitation near 1.8 meV was also observed in anion conducting superionic conductor CsPbBr3 by the inelastic neutron scattering measurements. The results suggest that the presence of the low-lying dispersionless excitation would be related to the mass of heavy cations in CsPbX3 (X=Cl, Br).