  The scattering of Dirac particles by symmetric potentials in one dimension is
studied. A Levinson theorem is established. By this theorem, the number of
bound states with even (odd) parity, $n_+$ ($n_-$), is related to the phase
shifts $\eta_+(\pm E_k)$ [$\eta_-(\pm E_k)$] of scattering states with the same
parity at zero momentum as follows: $$\eta_\pm(\mu)+\eta_\pm(-\mu)\pm{\pi\over
2}[\sin^2\eta_\pm(\mu) -\sin^2\eta_\pm(-\mu)]=n_\pm\pi.$$ The theorem is
verified by several simple examples.
