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Second-order topological insulator, which has (d-2)-dimensional topological hinge or corner states, has been observed in three-dimensional materials, but has yet not been observed in two-dimensional system. In this Letter, we theoretically propose the realization of second-order topological insulator in the van der Waals heterostructure of CoBr$_2$/Pt$_2$HgSe$_3$/CoBr$_2$. Pt$_2$HgSe$_3$ is a large gap $\mathbb{Z}_2$ topological insulator. With in-plane exchange field from neighboring CoBr$_2$, a large band gap above 70 meV opens up at the edge. The corner states, which are robust against edge disorders and irregular shapes, are confirmed in the nanoflake. We further show that the second-order topological states can also be realized in the heterostructure of jacutingaite family $\mathbb{Z}_2$ topological insulators. We believe that our work will be beneficial for the experimental realization of second-order topological insulators in van der Waals layered materials.