Melt blowing, a commercialized polymer processing technique, is used to produce a majority of nonwoven fiber products. It utilizes a stream of hot air to attenuate an extruded polymer strand into a fiber that is typically larger than 1 μm in diameter. Recently, our group has demonstrated the capability of melt blowing various polymers into defect-free fibers with an average diameter of several hundred nanometers by using a lab scale melt blowing device designed after a typical commercial instrument. However, surface tension-driven instabilities are observed when the smallest fibers are generated, resulting in droplets dispersed in the fiber mat. We hypothesize that altering the rheological properties of polymer may either delay or suppress these instabilities. In this study, the rheology has been studied systematically by melt blowing bidisperse polymeric blends obtained by mixing low and high molecular weight polymer. The associated changes in the rheological properties and the effect of rheology on the average and the width of the fiber diameter distribution will be highlighted.