Polymer micro-/nanofibers, due to their low-cost and mechanical flexibility, are attractive building blocks for developing lightweight and flexible optical circuits. They are also versatile photonic materials for making various optical resonators and lasers, such as microrings, networks and random lasers. In particular, for random lasing architectures, the demonstrations to-date have mainly relied on fiber bundles whose properties are hard to tune post-fabrication. Here, we demonstrate the successful implementation of an inverted photonic glass structure with monodisperse pores of 1.28 μm into polymer fibers with diameter ranging from 10 to 60 μm. By doping organic dye molecules into this structure, individual fibers can sustain random lasing under optical pulse excitation. The dependence of lasing characteristics, including lasing spectrum and lasing threshold on fiber diameter are investigated. It is found that the lasing emission red-shifts and the threshold decreases with increasing fiber diameter. Furthermore, owing to the mechanical flexibility, the lasing properties can be dynamically changed upon stretching, leading to a wavelength-tunability of 5.5 nm. Our work provides a novel architecture for random lasers which has the potential for lasing tunability and optical sensing.