Combination therapy by co-delivering multiple drugs using a single delivery carrier is a promising strategy to achieve a synergistic antitumor effect. In this study, a novel dual-functional block copolymer mPEG--poly(TAC--ATMC--S(CH)COOH) was designed and synthesized for co-delivering two kinds of anticancer drugs, methotrexate (MTX) and doxorubicin (DOX). This biodegradable amphiphilic copolymer could spontaneously self-assemble into electronegative nanomicelles with higher micelle stability and lower hemolysis ratio. Besides hydrophobic interactions, electrostatic interactions between the carboxyl groups of 5-allyloxy-1,3-dioxan-2-one (ATMC) with amine groups of DOX, as well as complementary multiple hydrogen-bonding interactions between thymine groups of thymine-functional six-membered cyclic carbonate (TAC) and 2,6-diaminopyridine (DAP) groups of MTX, could contribute to co-delivering DOX/MTX simultaneously with high-efficiency loading without interference with each other. For comparison, DOX alone and MTX alone were also encapsulated into mPEG--poly(TAC--ATMC--S(CH)COOH) nanomicelles. All drug-loaded nanomicelles exhibited sustained release properties with a pH sensitivity. Confocal laser scanning microscopy revealed an efficient cell uptake of DOX and MTX delivered by mPEG--poly(TAC--ATMC--S(CH)COOH) nanomicelles, while DOX mainly accumulated in nuclei and MTX in cytoplasm after 8 h of incubation. MTT assay further demonstrated an enhanced synergistic antitumor efficacy of DOX/MTX co-loaded nanomicelles. Therefore, DOX/MTX co-loaded mPEG--poly(TAC--ATMC--S(CH)COOH) nanomicelles might have attractive potentials in clinical implications for efficient combination chemotherapy.