There is weak source-load matching and inadequate energy storage application in a microgrid. It needs to coordinate and optimize the source-load and energy storage considering the demand-side management and carbon emission. In this paper, the optimization of a grid-connected microgrid is divided into two stages including demand-side management and dispatching. First, in the first stage, a demand-side management model is introduced. The energy storage battery is considered and a crisscross optimization algorithm is used to minimize the net load of the microgrid and maximize the self-supply rate. Then, in the second stage, from the economy and environmental protection perspective, a wind, photovoltaic, micro-gas turbine, fuel cell and storage energy microgrid day-ahead optimal dispatching model is established to minimize total costs and carbon emissions. It relies on the information after the demand-side management in the first stage. The above model is analyzed using the improved multi-objective gray wolf optimization algorithm. Finally, taking an actual microgrid in Fujian as an example, simulation shows that the introduction of demand-side management can effectively use energy storage batteries to improve the matching degree of microgrid source-load and fully tap the demand response potential. Compared with single-stage optimization, two-stage optimization is more conducive to improving the penetration rate of renewable energy, reducing the daily operating costs and carbon emissions of microgrids, and realizing their low-carbon economic operation. This work is supported by the National Natural Science Foundation of China (No. 51977039).