Hydrogels have recently received attention as delivery carriers owing to their good biocompatibility and structural similarity to natural extracellular matrices. However, the utilization of traditional single-network (SN) hydrogels is limited by poor mechanical properties and burst drug release. Therefore, we developed a novel double-network (DN) hydrogel, which employs an alginate (ALG)/polyethylene glycol diacrylate (PEGDA) network to adjust the mechanical strength and a positively charged monomer AETAC (2-(acryloyloxy)ethyl]trimethyl-ammonium chloride) to regulate the release curve of the electronegative anti-human papillomavirus (HPV) protein (bovine β-lactoglobulin modified with 3-hydroxyphthalic anhydride) based on an affinity-controlled delivery mechanism. The results show that the double-network hydrogel strongly inhibits the burst release, and the burst release amount is about one-third of that of the single-network hydrogel. By changing the concentration of the photoinitiator, the mechanical strength of the DN hydrogels can be adjusted to meet the stiffness requirements for various tissues within the range of 0.71 kPa to 10.30 kPa. Compared with the SN hydrogels, the DN hydrogels exhibit almost twice the mechanical strength and have smaller micropores. Cytotoxicity tests indicated that these SN and DN hydrogels were not cytotoxic with the result of over 100% relative proliferation rate of the HUVECs. Furthermore, DN hydrogels can significantly alleviate the burst release of antiviral proteins and prolong the release time to more than 14 days. Finally, we utilized digital light processing (DLP) technology to verify the printability of the DN hydrogel. Our study indicates that ALG/PEGDA-AETAC DN hydrogels could serve as platforms for delivering proteins and show promise for diverse tissue engineering applications.