If $G$ is an $(n,m)$-graph whose spectrum consists of the numbers $\lambda_1,\lambda_2,\ldots,\lambda_n$, then its Estrada index is $\operatname{EE}(G)=\sum_{i=1}^n e^{\lambda_i}$. We establish lower bounds for $\operatorname{EE}(G)$ in terms of $n$ and $m$.