The resistance of cancer cells to anticancer drugs has been recognized as one of the main reasons for chemotherapy failure. Multidrug combination therapy is one of the most effective ways to solve this problem. Therefore, in this article, we designed and synthesized a pH/GSH dual-responsive camptothecin/doxorubicin (CPT/DOX) dual pro-drug synergistic treatment system with the aim of overcoming the resistance of non-small cell lung cancer A549/ADR cells to DOX. The pro-drug cRGD-PEOz-S-S-CPT (cPzT) was obtained by linking CPT to poly(2-ethyl-2-oxazoline) (PEOz) with endosomal escape properties through a GSH-responsive disulfide bond and modifying it with the targeted peptide cRGD. The pro-drug mPEG-NH-N=C-DOX (mPX) was synthesized by attaching DOX to polyethylene glycol (PEG) through acid-sensitive hydrazone bonds. The dual pro-drug micelles cPzT/mPX configured according to the CPT/DOX mass ratio of 3:1 showed a strong synergistic therapeutic effect at IC50 with a combined therapy index CI = 0.49, far less than 1. Moreover, with the further improvement of the inhibition rate, the 3:1 ratio showed a stronger synergistic therapeutic effect than other ratios. The cPzT/mPX micelles not only had better targeted uptake ability but also showed a better therapeutic effect in both 2D and 3D tumor suppression assays relative to free CPT/DOX and significantly enhanced the penetration ability into solid tumors. In addition, the results of confocal laser scanning microscopy (CLSM) showed that cPzT/mPX could effectively overcome the resistance of A549/ADR cells to DOX by delivering DOX into the nucleus to exert its effect. Thus, this dual pro-drug synergistic therapy system combining targeting and endosomal escape ability provides a possible strategy to overcome tumor drug resistance.