With an increasing number of controllable distributed energy resources deployed and integrated into the power system, how to economically manage these distributed resources will become a challenge for the future smart grid. To solve the issue, consensus based distributed economic dispatch algorithms have been introduced in the literature as computationally scalable approaches. However, in real-world applications with imperfect communications networks, the performance of consensus-based economic dispatch algorithms degrades when information losses occur. In this paper, a robust distributed system incremental cost estimation (RICE) algorithm is introduced to solve the Economic Dispatch Problem (EDP) in a smart grid environment in a distributed way considering communications information losses. Unlike the existing consensus-based algorithms to solve EDP, RICE algorithm has two updating layers running in parallel in each distributed controller: one layer uses the gossip updating rule to estimate the system's average power mismatch, while the other layer uses the consensus updating rule to update the system Incremental Cost (IC) estimation. In this approach, the vulnerability of consensus-based algorithms to communications information losses is eliminated. The convergence and optimality of the algorithm are guaranteed as long as the undirected communications topology among local controllers is connected. Several case studies are presented to illustrate the performance of the proposed algorithm, and show the robustness under different information loss scenarios with different communications topologies. Display Omitted The classic Economic Dispatch Problem is solved in a distributed manner.The proposed RICE algorithm is robust to communication information losses.The proposed RICE algorithm is highly scalable.Rigorous analysis is provided to prove the convergency and optimality.