This paper studies the problem of distributed economic dispatch for smart grids under heterogeneous time delays. We design a state predictor for each agent to compensate the effect of heterogeneous time delays. This predictor allows the agents to predict the missing states between two consecutive update times. Based on the predictor, we propose a distributed gradient-descent algorithm to locally update the outputs of the generators, which avoids the update of the Lagrange multiplier of the supply-demand-balance constraint. We show that the optimal solution is achieved asymptotically under the proposed predictive optimization scheme. The effectiveness of the theoretical results is verified by numerical examples based on the IEEE 6-bus test platform.