  The Estrada index of a graph $G$ is defined as
$EE(G)=\sum_{i=1}^ne^{\lambda_i}$, where $\lambda_1,$ $ \lambda_2,\ldots,
\lambda_n$ are the eigenvalues of the adjacency matrix of $G$. In this paper,
we characterize the unique bipartite graph with maximum Estrada index among
bipartite graphs with given matching number and given vertex-connectivity,
edge-connectivity, respectively.
