This paper focuses on developing an adaptive communication and control co-design approach for the coordination of networked agents with second-order dynamics. In contrast to the existing results on coordination of networked agents based on the assumption that the network topology is modeled using either communication-free models or fixed communication ranges, we propose to develop a new control technique to adjust the communication range of each agent and agents' motion adaptively. In order to derive the adaptive communication control law for each agent, the existing cooperative control algorithms cannot be applied due to the need for predicting agents' future behavior. We first redesign the cooperative control algorithm and then derive an explicit bound to determine the communication ranges needed for all agents. Then rigorous analysis is provided to show the convergence of the new adaptive communication and control algorithms. Simulation examples are finally provided to show the effectiveness of the proposed algorithms and its comparison with some existing algorithm on energy efficiency.