The efficient intracellular drug delivery is an important challenge due to the slow endocytosis and inefficient drug release of traditional delivery vehicles such as symmetrical polymer vesicles, which have the same coronas on both sides of the membrane. Presented in this paper is a noncytotoxic poly(ethylene oxide)-block-poly(caprolactone)-block-poly(acrylic acid) (PEO113-b-PCL132-b-PAA(15)) triblock copolymer vesicle with an asymmetrical structure. The biocompatible exterior PEO coronas are designed for stealthy drug delivery; The pH-responsive interior PAA chains are designed for rapid endosomal escape and enhanced drug loading efficiency. The hydrophobic PCL vesicle membrane is for biodegradation. Such asymmetrical polymer vesicle showed high doxorubicin (DOX) loading efficiency and good biodegradability under extracellular enzymatic conditions. Compared with three traditional symmetrical vesicles prepared from PEO113-b-PCL110, PEO43-b-PCL98-b-PAA(25), and PAA(21)-b-PCL75 copolymers, the DOX-loaded asymmetrical PEO113-b-PCL132-b-PAA(15) polymer vesicles exhibited rapid endocytosis rate and much faster endosomal escape ability, demonstrating promising potential applications in nanomedicine.