Aiming at the economic dispatching problem with privacy guarantees and unknown gradient information in microgrid, a distributed online economic dispatching algorithm based on differential privacy mechanism and one-point feedback is proposed in this paper. Different from most existing researches on economic dispatching algorithms ignoring privacy protection, this paper introduces random noise which conforms to the Laplacian distribution to disturb the state of nodes, which effectively protects the privacy information of nodes. The algorithm estimates the real gradient information based on one-point feedback to guide the updating of decision variables, avoids accurate gradient calculation, and is suitable for the scenario where gradient information is unavailable. In addition, the economic dispatching problem is extended to the distributed online framework to adapt to the time-varying cost function scenario. Under the proposed algorithm, the economic dispatching problem can be solved in an online way, and the algorithm can achieve the same sublinear rate regret . Finally, the effectiveness of the algorithm is verified by simulation results.