In this study, we report a facile approach to develop composite nanofibrous mat for tissue engineering application. Montmorillonite (MMT) nanoparticles were first used to load an antipyretic analgesic drug, aspirin (ASP). The ASP-loaded MMT nanohybrids were mixed with polyurethane (PU) for subsequent electrospinning to form drug-loaded PU/MMT/ASP composite nanofibrous mats. Then electrospun PU/MMT/ASP nanofibers were assembled with a bilayer of polyacrylic acid (PAA) and poly(ethylene imine) (PEI) through electrostatic interaction. Silver nanoparticles have been immobilized onto nanofibrous mats by in situ complexation and chemical reduction of AgNO3 solution to form PU/MMT/ASP/Ag nanofibrous mats. The PU/MMT/ASP/Ag composite nanofibrous mats were systematically characterized using scanning electron microscopy (SEM), Fourier transform infrared spectroscopy, and mechanical testing. In vitro drug release showed that this composite nanofibrous drug delivery system can effectively mitigate the burst release of the drug and the introduction of MMT can improve the tensile stress property. Further the antibacterial properties and cytotoxicity evaluation of these mats demonstrate that the PU/MMT/ASP/Ag has a reasonable activity toward the growth inhibition of model bacterium Staphylococcus aureus, and the PU/MMT/ASP/Ag nanofibers display good cytocompatibility. In view of its sustained release profile and excellent biocompatibility, this double-loaded drug delivery system may have great prospect in tissue engineering.