Recent progress in nanostructuring of materials opens up possibilities to achieve more efficient thermoelectric devices. Nanofilms, nanowires, and nanorings may show increased phonon scattering while keeping good electron transport, two of the basic ingredients for designing more efficient thermoelectric systems. Here we argue that graphene nanorings attached to two leads meet these two requirements. Using a density-functional parametrized tight-binding method combined with Green's function technique, we show that the lattice thermal conductance is largely reduced as compared to that of graphene nanoribbons. At the same time, numerical calculations based on the quantum transmission boundary method, combined with an effective transfer matrix method, predict that the electric properties are not considerably deteriorated, leading to an overall remarkable thermoelectric efficiency. We conclude that graphene nanorings can be regarded as promising candidates for nanoscale thermoelectric devices.