Three-dimensional bioprinting is an emerging technology for fabricating living 3D constructs, and it has shown great promise in tissue engineering. Bioinks are scaffold materials mixed with cells used by 3D bioprinting to form a required cell-laden structure. In this paper, a novel bioink made of gelatin methacrylamide (GelMA) and collagen (Col) doped with tyrosinase (Ty) is presented for the 3D bioprinting of living skin tissues. Ty has the dual function of being an essential bioactive compound in the skin regeneration process and also as an enzyme to facilitate the crosslink of Col and GelMA. Further, enzyme crosslinking together with photocrosslinking can enhance the mechanical strength of the bioink. The experimental results show that the bioink is able to form stable 3D living constructs using the 3D bioprinting process. The cell culture shows that three major cell lines: human melanocytes (HEM), human keratinocytes (HaCat) and human dermal fibroblasts (HDF) exhibit high cell viabilities. The viability of these three cell lines is above 90%. The proliferation and scratching test show that Ty can enhance the proliferation of HEM, inhibit the growth and migration of HDF and not affect HaCat significantly. Animal tests show that the doped bioinks for 3D bioprinting can help form an epidermis and dermis, and thus have high potential as a skin bioink.