Inorganic-organic composite hydrogels have attracted much attention in recent years. In this study, an amino-functionalized graphene/alginate double-network hydrogel (NH-DN) with excellent mechanical and adsorption properties was successfully prepared. Triethylenetetramine (TETA) was used as a crosslinker which promotes random few-layer graphene sheets stacking and resulted in a reduced graphene oxide (rGO) network, containing mesopore and macropore structures on the hydrogel surface. Compared to single network hydrogel, enhanced thermal stability and mechanical properties were achieved in NH-DN. The elasticity modulus was improved by approximately 3 times due to the formation of the double-network. More importantly, NH-DN exhibited excellent adsorption properties for typical emerging contaminants (Cu and ciprofloxacin (CIP)). Compared with that of an ordinary graphene/alginate single-network hydrogel (SN), the adsorption capacity of the NH-DN for Cu and CIP reached 153.91 mg g and 301.36 mg g, respectively, which was increased by 130% and 182%, respectively. Adsorption isotherm and kinetic analyses reveal that the adsorption process of CIP onto the NH-DN was dominated by chemical affinity. Adsorption properties were comprehensively examined, including the effects of the solid-liquid ratios, pH, and ionic strength. NH-DN retained 94% of its adsorption capacity when the ionic strength was 0.5 mol L and maintained at least 87% of its adsorption capacity in weak acidic and alkaline solutions. This novel amino-functionalized organic-inorganic hydrogel has great potential in environmental applications owing to its outstanding physicochemical, mechanical, and adsorption properties for emerging contaminants in wastewater.