In the context of the “dual-carbon” policy and multi-energy integration, integrated energy system (IES) has emerged. The advancement of related technologies has gradually upgraded the form of the IES, and with the driving force of national policies and the increasing maturity of hydrogen storage technologies, The integrated energy system incorporating hydrogen storage (HES-IES) has emerged as one of the crucial paths for the advancement within the energy domain. In order to promote the low-carbon economic operation of the IES, a multi-objective robust optimization model for the HES-IES considering the source-load uncertainty is proposed. The multi-objective optimization functions are chosen to be the minimum operating cost and carbon emission of the system, the model is solved by the combination of compromise planning and the maximum-minimum fuzzy method. Finally, the actual data from a certain place in Hebei Province is used for validation, and the results indicate that the model put forward is capable of efficiently striking a balance between the economy and environmental conservation.