We have investigated the phonon and the magnetic excitations in LaCoO3 by inelastic neutron scattering measurements. The acoustic phonon dispersions show some characteristic features of the folded Brillouin zone (BZ) for the rhombohedrally distorted perovskite structure containing two chemical formula units of LaCoO3 in the unit cell. We observed two transverse optical (TO) phonon branches along (delta, delta, delta), consistent with previously reported Raman active Eg modes which show remarkable softening associated with the spin-state transition [Ishikawa et al., (Phys. Rev. Lett. 93 (2004) 136401.)]. We found that the softening takes place in the TO mode over the whole BZ. In contrast, the acoustic phonons show no anomalous softening associated with the spin-state transition. The low-energy paramagnetic scattering at 8 K is weak, increasing towards a maximum at E > 15 meV, consistent with excitation of the nonmagnetic low-spin to magnetic intermediate-spin state of Co 3+ ions.