  We calculate the pion-nucleon scattering lengths $a_{0}^{(\pm)}$ and the mass
parameter $m_{0}$, which describes the nucleon mass in the chiral limit, at
tree-level in the framework of a globally symmetric linear sigma model with
parity-doubled nucleons. When recent lattice results [Takahashi] are used, we
obtain $m_{0}\simeq300-600$ MeV. While $a_{0}^{(-)}$ is in fair agreement with
experimental data, $a_{0}^{(+)}$ is too small because of the employed large
scalar meson mass. This indicates the need to account for additional scalar
degrees of freedom.
