An LED lamp may include at least one support equipped with at least one LED, a lamp base, at least one circuit component, interposed between the lamp base and the at least one LED, for operating the at least one LED, and a lamp body made of optically transmissive material with a recess for holding at least that part of the support which carries the at least one LED, the lamp body having surface structuring for cooling by thermal convection, wherein the surface structuring comprises a multiplicity of elevations, and wherein the elevations are respectively designed in the form of islands.