  We show a zero-gap semiconducting (ZGS) state in the quasi-two-dimensional
organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ salt, which emerges under
uniaxial pressure along the a-axis (the stacking axis of the BEDT-TTF
molecule). The ZGS state is the state in which a Dirac cone with the band
spectrum of a linear dispersion exists around the Fermi point connecting an
unoccupied (electron) band with an occupied (hole) band. The spectrum exhibits
a large anisotropy in velocity, which depends on the direction from the Fermi
point. By varying the magnitude of several transfer energies of a tight-binding
model with four sites per unit cell, it is shown that the ZGS state exists in a
wide pressure range, and is attributable to the large anisotropy of the
transfer energies along the stacking axis.
