A connected graph is called a bi-block graph if each of its blocks is a complete bipartite graph. Let $\mathcal{B}(\mathbf{k}, α)$ be the class of bi-block graph on $\mathbf{k}$ vertices with given independence number $α$. It is easy to see that every bi-block graph is a bipartite graph. For a bipartite graph $G$ on $\mathbf{k}$ vertices, the independence number $α(G)$ satisfies $\ceil*{\frac{\mathbf{k}}{2}} \leq α(G) \leq \mathbf{k}-1$. In this article, we prove that the maximum spectral radius $ρ(G)$ among all graphs $G$ in $\mathcal{B}(\mathbf{k}, α)$, is uniquely attained for the complete bipartite graph $K_{α, \mathbf{k}-α}$.