There are problems with the classical consensus algorithm in microgrid optimal dispatching in that it requires a centralized processor to collect and sum the information of the controllable units. Thus a completely distributed optimal scheduling strategy based on a consensus algorithm and gradient descent is proposed. The consensus principle of the algorithm consists of two parts: a consensus term and an adjustment term. The consensus term selects incremental cost as the state variable for iterative calculation. The adjustment term is corrected according to the power deviation to meet the constraints. This paper combines the gradient descent with the consensus principle to optimize the power generation cost of the microgrid and improve the convergence speed. In addition, the parameters can be updated through local information interaction between the controllable unit and the adjacent controllable unit to flexibly cope with a change of topology. Finally, the effectiveness and feasibility of the proposed method are verified by system simulation results of IEEE-14 nodes and IEEE-39 nodes. This work is supported by the General Program of National Natural Science Foundation of China (No. 61873159).