A new type of hydrogels based on poly(styrene-alt-maleic anhydride) (PSMA) was prepared via Diels-Alder click chemistry. The formulations consisting of tetrazine-functionalized PSMA as a multi-clickable polymer and norbornene-terminated poly(ethylene glycol) (PEG) as a polymeric cross-linker were used as precursors to give ultrafast hydrogels with controlled structures. The hydrogels formed within several minutes under a physiological condition without any catalyst, and their storage modulus (G′) values were in the range 0.3–1.7 kPa suitable for bio-applications. The pore structure and the release profile of doxorubicin hydrochloride (DOX·HCl) of the hydrogels could be manipulated by the molecular weight of PEG. The precursors exhibited practically no depressing effect of the normal HEK293 growth, while the DOX·HCl-loaded hydrogel presented significant anticancer activity towards HeLa cells. The results suggested this biocompatible hydrogel as a potential injectable drug depot for tumor sites.