  The pairing symmetry is one of the major issues in the study of iron-based
superconductors. We adopt a low-energy effective kinetic model based on the
first-principles band structure calculations combined with the $J_1$-$J_2$
model for KFe$_2$As$_2$, the phase diagram of pairing symmetries is
constructed. Putting the values of $J_1$ and $J_2$ of the $J_1$-$J_2$ model
obtained by the first-principles calculations into this phase diagram, we find
that the pairing symmetry for KFe$_2$As$_2$ is a nodal $d_{xy}$-wave in the
folded Brillouin zone with two iron atoms per unit cell. This is in good
agreement with experiments observed a nodal order parameter.
