The purpose of this work was to develop a type of tissue-engineering scaffold or drug-delivery carrier with the capability of encapsulation and controlled release of dual drugs. In this study, Rhodamine B and bovine serum albumin (BSA) were successfully incorporated into nanofibers by means of blending or coaxial electrospinning. The morphology of composite nanofibers was studied by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The composite nanofibrous mats made from coaxial electrospinning were characterized by X-ray diffraction. In vitro dual-drug release behaviors from composite nanofibrous mats were investigated. From the drug-release profiles, it shows that the location where the drug or protein is put into (into the core or shell of the nanofibers) can affect the drug-release profile in the coaxially electrospun fibers. The results imply that the drug- and/or protein-release profile in composite fibrous mats made from electrospinning can be controlled by altering the coaxial electrospinning process and has significant implications for a wide range of applications such as tissue regeneration, combined therapies or even cancer treatments.