  After the discovery of the $s$-wave and $p$-wave holographic superconductors,
holographic models of $d$-wave superconductor have also been constructed
recently. We study analytically the perturbation of the dual gravity theory to
calculate the superconducting coherence length $\xi$ of the $d$-wave
holographic superconductor near the superconducting phase transition point. The
superconducting coherence length $\xi$ divergents as $(1-T/T_c)^{-1/2}$ near
the critical temperature $T_c$. We also obtain the magnetic penetration depth
$\lambda\propto(T_c-T)^{-1/2}$ by adding a small external homogeneous magnetic
field. The results agree with the $s$-wave and $p$-wave models, which are also
the same as the Ginzburg-Landau theory.
