Polarized neutron inelastic scattering has been used to measure spin excitations in ferromagnetic La$_{0.82}$Sr$_{0.18}$CoO$_{3}$. The magnon spectrum of these spin excitations is well defined at low energies but becomes heavily damped at higher energies, and can be modeled using a quadratic dispersion. We determined a spin wave stiffness constant of $D=94pm 3$,meV,AA$^{2}$. Assuming a nearest-neighbor Heisenberg model we find reasonable agreement between the exchange determined from D and the bulk Curie temperature. Several possible mechanisms to account for the observed spin-wave damping are discussed.