Silicene, a novel graphene-like material, has attracted a significant attention because of its potential applications for nanoelectronics. In this paper, we have theoretically investigated the structural stability of edge-hydrogenated and edge-fluorinated silicene nanoribbons (SiNRs) via first-principles calculations. Various edge forms of SiNRs including armchair edge, zigzag edge, Klein edge, reconstructed Klein edge, reconstructed pentagon-heptagon edge, and hybrid edges have been considered. It has been found that fully fluorinated Klein edge SiNRs, in which each edge Si atom is terminated by three fluorine atoms, are the most stable structure. We also discovered that a hybrid edge structure of trihydrogenated Klein edge and dihydrogenated zigzag edge can increase the nanoribbon’s stability up to that of dihydrogenated armchair edge SiNR, which is known as the most stable edge-hydrogenated structure. With the attractive properties of silicene for practical applications, the obtained results will advance experimental investigations toward the development of silicene based devices.