Reduction-responsive core-crosslinked micelles were developed based on a glycol chitosan–lipoic acid (GC–LA) conjugate and used for triggered release of doxorubicin (DOX). The substitution degree of GC–LA was 8.3 lipoic acid groups per 100 sugar units of glycol chitosan. GC–LA could form nanoscaled micelles in aqueous solution, wherein the critical micelle concentration (CMC) of 0.081 mg mL−1 was determined. Furthermore GC–LA micelles can be crosslinked by a catalytic amount of dithiothreitol. The mean diameter of DOX-loaded core-crosslinked GC–LA (DOX-GC–LA/cc) micelles increased from 305 to 408 nm as the DOX-loading content increased from 6.03% to 10.74%. DOX-loaded crosslinked micelles demonstrated obvious reduction-triggered destabilization. DOX release from non-crosslinked GC–LA micelles was 87.6% for up to 96 h, whereas 25.3% of DOX release from DOX-GC–LA/cc micelles was observed in phosphate buffered saline (PBS, pH 7.4). Notably, in the presence of a 20 mM GSH-containing environment, accelerated DOX release from DOX-GC–LA/cc micelles was found. The blank micelles had low cytotoxicity in vitro, and DOX-GC–LA/cc micelles demonstrated intracellular redox-responsive characteristics in A549 cancer cells. These results suggested that GC–LA core-crosslinked micelles could be promising carriers for anticancer drug delivery.