The high water content and biocompatibility of amino-acid-based supramolecular hydrogels have generated growing interest in drug delivery research. Nevertheless, the existing dominant approach of constructing such hydrogels, the exploitation of a single amino acid type, typically comes with several drawbacks such as weak mechanical properties and long gelation times, hindering their applications. Here, we design a near-infrared (NIR) light-responsive double network (DN) structure, containing amino acids and different synthetic or natural polymers, i.e., polyacrylamide, poly(N-isopropylacrylamide), agarose, or low-gelling agarose. The hydrogels displayed high mechanical strength and high drug-loading capacity. Adjusting the ratio of Fmoc-Tyr-OH/Fmoc-Tyr(Bzl)-OH or Fmoc-Phe-OH/Fmoc-Tyr(Bzl)-OH, we could drastically shorten the gelation time of the DN hydrogels at room and body temperatures. Moreover, introducing photothermal agents (graphene oxide, carbon nanotubes, molybdenum disulfide nanosheets, or indocyanine green), we equipped the hydrogels with NIR responsivity. We demonstrated the light-triggered release of the drug baclofen, which is used in severe spasticity treatment. Rheology and stability tests confirmed the positive impact of the polymers on the mechanical strength of the hydrogels, while maintaining good stability under physiological conditions. Overall, our study contributed a novel hydrogel formulation with high mechanical resistance, rapid gel formation, and efficient NIR-controlled drug release, offering new opportunities for biomedical applications.