In order to achieve the passive tumor targeting and acid-triggered drugs release in lysosomes, optimized delivery system for doxorubicin based on pH-sensitive complex nanomicelles with suitable particle size was developed in this research. Particularly, poly(L-succinimide) was thoroughly ring-opened by ethylenediamine to give the poly(N-(2-aminoethyl)-L-aspartamide). Then, graft copolymer mPEG-graft-poly(N-(2-aminoethyl)-L-aspartamide)-hexahydrophthalic acid (mPEG-g-P(ae-Asp)-Hap) was synthesized by grafting mPEG-2000 and hexahydrophthalic anhydride onto poly(N-(2-aminoethyl)-L-aspartamide). In vitro studies revealed that mPEG-g-P(ae-Asp)-Hap copolymer was stable in neutral solutions but tend to be hydrolyzed under acidic condition, which was attributed to the acid-sensitive properties of hexahydrophthalic amides (β-carboxylic amides). MPEG-g-P(ae-Asp)-Hap copolymer with critical aggregation concentration of 0.166 mg·mL could self-assemble into stable blank nanomicelles with an average particle hydrodynamic diameter of 98.1 nm, but the hydrodynamic diameter of doxorubicin-loaded nanomicelles (mPEG-g-P(ae-Asp)-Hap·Dox) was smaller and approximately 77.5 nm. MPEG-g-P(ae-Asp)-Hap·Dox nanomicelles showed sustained drug release profiles over 34 h, and the cumulative drug release showed a tendency to increase from 25% to 62% with the pH value decreasing from 7.4 to 5.0 due to the acid-triggered disassembly of nanomicelles. The cytotoxicity of mPEG-g-P(ae-Asp)-Hap·Dox nanomicelles against A549 treated with 40 mM NHCl (lysosomotropic weak bases) was decreased significantly than that without NHCl treatment, further confirmed the drug release from the nanomicelles was triggered by the low pH value of lysosome (pH 5.0). Compared with doxorubicin HCl, mPEG-g-P(ae-Asp)-Hap·Dox nanomicelle drug showed enhanced cellular uptake ability during 2 or 4 h of incubation due to the endocytosis mechanism of nanomicelle drug. In summary, the cleavage of pH-sensitive β-carboxylic amides bonds on the hydrophobic branch of mPEG-g-P(ae-Asp)-Hap copolymer triggered the disassembly of the nanomicelles and release of doxorubicin in the acidic lysosomal compartments of cancer cells. These nanomicelles exhibited excellent potential for drug delivery due to their smart properties-PEGylation, suitable size, and acid-triggered drug release.