In this paper, we consider the problem of Voronoi-based coverage control for multi-robot sensor networks with connectivity constraints, where a team of mobile robots spread out over the workspace in order to optimize the overall coverage performance while preserving connectivity. In particular, we proposed a connectivity-aware coverage control approach to simultaneously optimize the coverage performance and ensure robotic network connectivity. Unlike most of existing works on connectivity control that have no guarantee on the primary task, our algorithm could maintain minimum connectivity that introduce minimal revision to the primary coverage controller due to invoked connectivity constraints. This ensures the robotic network stay connected at all time but also in an optimal way to provide highest freedom for achieving primary coverage task. Moreover, we prove the convergence of the proposed controller that guarantees continuously improved coverage performance in presence of connectivity constraints. Simulation results are given to demonstrate the effectiveness of our approach.