The application of textile reinforced concrete is well-approved technique for strengthening of reinforced concrete members. When using carbon fiber meshes and carbon fiber reinforced polymer bars as reinforcement, this material is called carbon concrete composite. Based on the outstanding properties of carbon fibers, carbon concrete composite is characterized by high bending and tensile strength, and good durability. Therefore, carbon concrete composite is increasingly applied as replacement for ordinary steel bar or steel mesh reinforced concrete. It is favorable building material for production of new buildings and for strengthening of existing reinforced concrete members. In the context of strengthening of existing reinforced concrete columns, it is a usual procedure to cover the member’s surface with a thin layer of carbon concrete composite aiming on reduction of lateral strains of the core concrete when load is increasing. The result is an increased load-bearing capacity of the strengthened column. However, there is insufficient knowledge about the influence of curvature of the carbon meshes in circular cross-sections and in the corners of rectangular cross-sections on their load-bearing capacity. For this reason, an experimental program started to study the influence of curvature, number and type of mesh layers and specimen dimensions on structural behavior of strengthened columns under axial loading. As main outcome it can be stated that besides the curvature other parameters like yarn properties are of essential importance.