Spatial graphene is a 3D structure of a 2D material that preserves its main features. Its production can be originated from the water solution of graphene oxide (GO). The main steps of the method include the crosslinking of flakes of graphene via treatment with hydrazine, followed by the reduction of the pillared graphene oxide (pGO) with hydrogen overpressure at 700 °C, and further decoration with catalytic metal (palladium). Experimental research achieved the formation of reduced pillared graphene oxide (r:pGO), a porous material with a surface area equal to 340 m2/g. The transition from pGO to r:pGO was associated with a 10-fold increase in pore volume and the further reduction of remaining oxides after the action of hydrazine. The open porosity of this material seems ideal for potential applications in the energy industry (for hydrogen storage, in batteries, or in electrochemical and catalytic processes). The hydrogen sorption potential of the spatial graphene-based material decorated with 6 wt.% of palladium reached 0.36 wt.%, over 10 times more than that of pure metal. The potential of this material for industrial use requires further refining of the elaborated procedure, especially concerning the parameters of substrate materials.