Most of the energy demand at shrimp farms in Vietnam is consumed by the aeration system for maintaining suitable dissolved oxygen in ponds continuously. The intensive energy consumption from electric motors for aeration and pumping systems leads to high operation costs and associated greenhouse gas emissions from using conventional power resources. This paper, therefore, proposes an optimal microgrid by multi-objective functions for the shrimp aquaculture industry. The proposed system harnesses renewable energy resources to power the electrolyzer to produce pure oxygen in situ for oxygenation according to the changes of species under culture. In addition, the by-product hydrogen from the electrolysis process could be used for either commercial purposes or backup power. The mathematical models of the system were developed for simulation and optimization to assess the performance of the system regarding technical, economic, and environmental aspects as multi-objective functions in autonomous mode and on-grid mode. Besides, the optimal results showed that the sustainable hybrid energy system connecting to the national grid in which the by-product hydrogen is primarily either sold for commercial purposes or used for backup power could bring significant benefits for farmers thanks to a notable reduction in the annualized cost of the system as well as CO₂ emission in comparison with the conventional system run by common paddlewheel aerators.