Isocyanate-terminated adhesive amphiphilic block copolymers are attractive materials to treat meniscus tears due to their tuneable mechanical properties and good adhesive characteristics. However, a drawback of this class of materials is their relatively long curing time. In this study, we evaluate the use of an amine cross-linker and addition of catalysts as two strategies to accelerate the curing rates of a recently developed biodegradable reactive isocyanate-terminated hyper-branched adhesive block copolymer prepared from polyethylene glycol (PEG), trimethylene carbonate, citric acid and hexamethylene diisocyanate. The curing kinetics of the hyper-branched adhesive alone and in combination with different concentrations of spermidine solutions, and after addition of 2,2-dimorpholinodiethylether (DMDEE) or 1,4-diazabicyclo [2.2.2] octane (DABCO) were determined using FTIR. Additionally, lap-shear adhesion tests using all compositions at various time points were performed. The two most promising compositions of the fast curing adhesives were evaluated in a meniscus bucket handle lesion model and their performance was compared with that of fibrin glue. The results showed that addition of both spermidine and catalysts to the adhesive copolymer can accelerate the curing rate and that firm adhesion can already be achieved after 2 h. The adhesive strength to meniscus tissue of 3.2-3.7 N was considerably higher for the newly developed compositions than for fibrin glue (0.3 N). The proposed combination of an adhesive component and a cross-linking component or catalyst is a promising way to accelerate curing rates of isocyanate-terminated tissue adhesives.