Hyaluronic acid (HA)-based hydrogels are widely used in biomedical applications due to their excellent biocompatibility. HA can be Ultraviolet (UV)-crosslinked by modification with methacrylic anhydride (HA-MA) and crosslinked by modification with 3,3′-dithiobis(propionylhydrazide) (DTP) (HA-SH) via click reaction. In the study presented in this paper, a 3D-bioprinted, double-crosslinked, hyaluronic-acid-based hydrogel for wound dressing was proposed. The hydrogel was produced by mixing HA-MA and HA-SH at different weight ratios. The rheological test showed that the storage modulus (G’) of the HA-SH/HA-MA hydrogel increased with the increase in the HA-MA content. The hydrogel had a high swelling ratio and a high controlled degradation rate. The in vitro degradation test showed that the hydrogel at the HA-SH/HA-MA ratio of 9:1 (S9M1) degraded by 89.91% ± 2.26% at 11 days. The rheological performance, drug release profile and the cytocompatibility of HA-SH/HA-MA hydrogels with loaded Nafcillin, which is an antibacterial drug, were evaluated. The wound dressing function of this hydrogel was evaluated by Live/Dead staining and CCK-8 assays. The foregoing results imply that the proposed HA-SH/HA-MA hydrogel has promise in wound repair applications.