  We present a theoretical study on the superconductivity of
$\beta'$-(BEDT-TTF)$_2$ICl$_2$ at $T_{\rm c}=$14.2 K under a high hydrostatic
pressure recently found, which is the highest among organic superconductors. In
the present work, we study an effective model using the fluctuation-exchange
(FLEX) approximation based on the results of first-principles calculation. In
the obtained phase diagram, the superconductivity with $d_{xy}$-like symmetry
is realized next to the antiferromagnetic phase, as a result of the
one-dimensional to two-dimensional crossover driven by the pressure.
