Carbon materials with full sp2-hybridized buckling is a major challenge pervading fundamental nanoscience and nanotechnology research. Carbon atoms that are sp2 hybridized prefer to form hexagonal rings, such as in carbon nanotubes and graphene, which are low-dimensional materials. The incorporation of heptagonal, octagonal, and/or larger rings into a hexagonal sp2 carbon meshwork has been identified as a strategy for assembling three-dimensional (3D) sp2 carbon crystals, and one of the typical representatives are Schwarzite carbons, which possess a negative surface Gaussian curvature as well as unique physical properties. Herein, a 3D Schwarzite carbon consisting of only sp2-buckled heptagonal carbon rings, which is referred to as Hepta-carbon, is proposed based on first-principles calculations. Hepta-carbon is mechanically and thermodynamically stable, and energetically more favourable than experimental graphdiyne, fullerene C20 and most Schwarzite carbons under ambient conditions. Molecular dynamics simulations indicate that Hepta-carbon exhibits high-temperature thermostability up to 1500 K. Band structure and mechanical property simulations indicate that Hepta-carbon is a semi-metallic material with electron conduction and exhibits impressive mechanical properties such as high strength with quasi-isotropy, high incompressibility similar to diamonds, elastic deformation behaviour under uniaxial stress, and high ductility. Hepta-carbon presents a porous network with a low mass density of 1.84 g cm-3 and connected channels with diameters of 3.3-6.1 Å. Theoretical simulations of gas adsorption energy demonstrate that Hepta-carbon can effectively adsorb and stabilize greenhouse gases, including N2O, CO2, CH4, and SF6.