  We extend the formalism pioneered by Callan, Coote and Gross to investigate
the meson-meson scattering within the framework of 't Hooft model, i.e., the
two-dimensional QCD in the $N_c\to \infty$ limit. We derive the analytic
expressions for various two-body meson-meson scattering amplitudes,
concentrating on those quark diagrams which may be identified as the
meson-meson contact interaction vertex in the context of the mesonic effective
lagrangian in $1/N_c$ expansion. We also carry out a detailed numerical study
for the meson-meson scattering for various quark flavors, and observe the
near-threshold enhancement in some channels. This may be viewed as the hint of
the existence of the tetra-quark state below two-meson threshold.
