  We study Josephson effect of $d$-wave superconductor (DS)/ferromagnet
insulator(FI)/DS junctions on a surface of topological insulator (TI). We
calculate Josephson current $I\left(\varphi \right) $ for various orientations
of the junctions where $\varphi $ is the macroscopic phase difference between
two DSs. In certain configurations, we find anomalous current-phase relation
$I(\varphi)=-I\left( -\varphi +\pi \right)$ with $2\pi$ periodicity. In the
case where the first order Josephson coupling is absent without magnetization
in FI, $I(\varphi)$ can be proportional to $\cos \varphi$. The magnitude of the
obtained Josephson current is enhanced due to the zero energy states on the
edge of DS on TI. Even if we introduce an $s$-wave component of pair potential
in DS, we can still expect the anomalous current-phase relation in asymmetric
DS junctions with $I\left( \varphi =0\right) \neq 0$. This can be used to probe
the induced $d$-wave component of pair potential on TI surface in high-$T_{c}$
cuperate/TI hybrid structures.
