  In this paper, we study 2-complex symmetric composition operators with the
conjugation $J$ on the Hardy space $H^2$. More precisely, we obtain the
necessary and sufficient condition for the composition operator $C_\phi$ to be
2-complex symmetric when the symbols $\phi$ is an automorphism of $\mathbb D$.
We also characterize the 2-complex symmetric composition operator $C_\phi$ on
the Hardy space $H^2$ when $\phi$ is a linear fractional self-map of $\mathbb
D$.
