One of the most important properties of emulsions is their stability. Most emulsions stabilized with molecular surfactants tend to lose their stability over time via different mechanisms. Although the stability of emulsions stabilized with homogeneous particles have been shown to be superior to that of surfactant-stabilized emulsions, these Pickering emulsions nevertheless are only kinetically stable and thus can undergo destabilization. Janus particles that have two opposite wetting surfaces have shown promise in imparting emulsions with long-term stability because of their strong attachment to the oil-water interface. In this theoretical study, we consider thermodynamics of emulsion stabilization using amphiphilic Janus dumbbells, which are nonspherical particles made of two partially fused spherical particles of opposite wettability. These amphiphilic dumbbells are attractive candidates as colloid surfactants for emulsion stabilization because highly uniform Janus dumbbells can be synthesized in large quantities; thus, their application in emulsion stabilization can become practical. Our theoretical calculation demonstrates that Janus dumbbells can indeed generate thermodynamically stable Pickering emulsions. In addition, we also find that there exists a total oil-water interfacial area that results in the lowest energy state in the system, which occurs when Janus dumbbells available in the system are completely consumed to fully cover the droplet interfaces. We show that the geometry of dumbbells as well as the composition of the emulsion mixtures has significant influences on the average size of dumbbell-stabilized emulsions. We also investigate the effect of asymmetry of Janus dumbbells on the average droplet radius. Our results clearly show that amphiphilic Janus dumbbells provide unique opportunities in stabilizing emulsions for various applications.