The Micro-grid Operator (MGO) is the responsible of scheduling the available energy resources to provide the required energy of its customers. As a private entity, the micro-grid operators desire to specify the energy providing strategy in a way that maximizes its financial profit, which depends on the cost of supplying and income of selling energy to consumers. Residential consumers in smart distribution networks with bidirectional communication infrastructures are capable of adjusting their energy demands in response to electricity prices. Distinctly, falling/rising electricity tariffs decreases/increases the incomes of electricity MGOs and increases/decreases the energy demands of consumers due to their sensitivities to electricity tariffs. Accordingly, MGOs are responsible to retain a compromise between electricity tariffs and energy demands. MGO can participate in the electricity wholesale market or forward contracts to supply the demand of consumers. The expected profit of MGO is highly affected by the fluctuations of wholesale price. In this paper, the game theory (GT), as well as the robust optimization (RO) are used to obtain a robust energy procurement strategy for MGOs in smart distribution grids with hydrogen-based energy resources. The proposed hybrid GT+RO approach enables MGOs to obtain a robust energy procurement strategy hedged against different realizations of uncertain wholesale electricity prices. The energy procurement strategy of MGO is determined such that optimizes profits of customers and MGO, simultaneously. Case studies illustrate the effectiveness of the proposed robust energy procurement strategy under different circumstances.