  Let $(M,\omega_M)$ be a six dimensional closed monotone symplectic manifold
admitting an effective semifree Hamiltonian $S^1$-action. We show that if the
maximal and the minimal fixed component are both two dimensional, then
$(M,\omega_M)$ is $S^1$-equivariantly symplectomorphic to some K\"{a}hler Fano
manifold $(X, \omega_X, J)$ equipped with a certain holomorphic Hamiltonian
$S^1$-action. We also give a complete list of all such Fano manifolds together
with an explicit description of the corresponding $S^1$-actions.
