The corona product $GoH$ of two graphs $G$ and $H$ is defined as the graph obtained by taking one copy of $G$ and $|V(G)|$ copies of $H$ and joining the $i$-th vertex of $G$ to every vertex in the $i$-th copy of $H$. In this paper, the Szeged, vertex PI and the first and second Zagreb indices of corona product of graphs are computed.