In this work, we use molecular dynamics simulations to investigate coalescence-induced jumping of nanodroplets on curved surfaces with different wettabilities. On a curved surface, a liquid bridge will first form between two coalescing droplets as on a flat surface. However, contrary to symmetry-breaking-induced jumping on a flat surface, coalescing droplets would jump earlier than the liquid bridge gets into contact with the curved surface. Such an early symmetry breaking is induced by the opposite motion of coalescing droplets along the lateral direction on the curved surface. We find that surface curvature can effectively facilitate the jumping of coalescing nanodroplets via enhanced symmetry breaking. The energy conversion efficiency is improved from similar to 0.15% on a flat surface to similar to 2.9% on a curved surface, which is about 20 times enhancement. In addition, we conducted an energy scaling analysis by considering the lumped effects of both viscous dissipation and contact line friction on the jumping behaviors. We conclude that curvature-enhanced jumping in the nanoscale can be ascribed to the mitigated contact line dissipation E-cl, whereas viscous dissipation E-vis is maintained almost at the same level. Therefore, we unveil a scaling law between the energy conversion efficiency eta on surfaces with different curvatures and the product of contact line length and contact time. Interestingly, the increasing surface curvature could allow the occurrence of coalescence-induced jumping on a less superhydrophobic surface. Hence, a phase map of coalescence-induced jumping in terms of surface curvature ratio and surface wettability is presented. Essentially, the paradigm of curved surfaces in the nanoscale used in this study is characteristic of the topography of micro/nanostructured surfaces, on which coalescence-induced droplet jumping has been experimentally observed. This work justifies the critical role of nanoroughness in boosting coalescence-induced jumping of nanodroplets and sheds light on the passive control of nanodroplets jumping on functional surfaces.