A well-defined poly(ethylene glycol) based hyperbranched thermoresponsive copolymer with high content of acrylate vinyl groups was synthesized via a “one-pot and one-step” deactivation enhanced atom transfer radical polymerization approach, which provided an injectable and in situ crosslinkable system via Michael-type thiol-ene reaction with a thiol-modified hyaluronan biopolymer. The hyperbranched structure, molecular weight, and percentage of vinyl content of the copolymer were characterized by gel permeation chromatography and 1H NMR. The lower critical solution temperature of this copolymer is close to body temperature, which can result in a rapid thermal gelation at 37 °C. The scanning electron microscopy analysis of crosslinked hydrogel showed the network formation with porous structure, and 3D cell culture study demonstrated the good cell viability after the cells were embedded inside the hydrogel. This injectable and in situ crosslinking hybrid hydrogel system offers great promise as a new class of hybrid biomaterials for tissue engineering.