Controlling surface structure at the atomic scale is paramount to developing effective catalysts. For example, the edge sites of MoS2 are highly catalytically active and are thus preferred at the catalyst surface over MoS2 basal planes, which are inert. However, thermodynamics favours the presence of the basal plane, limiting the number of active sites at the surface. Herein, we engineer the surface structure of MoS2 to preferentially expose edge sites to effect improved catalysis by successfully synthesizing contiguous large-area thin films of a highly ordered double-gyroid MoS2 bicontinuous network with nanoscaled pores. The high surface curvature of this catalyst mesostructure exposes a large fraction of edge sites, which, along with its high surface area, leads to excellent activity for electrocatalytic hydrogen evolution. This work elucidates how morphological control of materials at the nanoscale can significantly impact the surface structure at the atomic scale, enabling new opportunities for enhancing surface properties for catalysis and other important technological applications.