Low-dimensional carbon allotropes, from fullerenes, carbon nanotubes, to graphene, have been broadly explored due to their outstanding and special properties. However, there exist significant challenges in retaining such properties of basic building blocks when scaling them up to three-dimensional materials and structures for many technological applications. Here we show theoretically the atomistic structure of a stable three-dimensional carbon honeycomb (C-honeycomb) structure with superb mechanical and thermal properties. A combination of sp(2) bonding in the wall and sp(3) bonding in the triple junction of C-honeycomb is the key to retain stability of C-honeycomb. The specific strength could be the best in structural carbon materials, and this strength remains at,a high level but tunable with different cell sizes. C-honeycomb is also found to have a very high thermal conductivity, for example, >100 W/mK along the axis of the hexagonal cell with a density only similar to 0.4 g/cm(3). Because of the low density and high thermal conductivity, the specific thermal conductivity of C-honeycoMbs is larger than most engineering materials, including metals and high thermal conductivity semiconductors, as well as lightweight CNT arrays and graphene-based nanocomposites. Such high specific strength, high thermal conductivity, and anomalous Poisson's effect in C-honeycomb render it appealing for the use in various engineering practices.