In recent years, 3D structures with negative Poisson's ratio (auxetic) have attracted great interest. Many polymer and metal 3D auxetic structures have been manufactured using additive manufacturing technology, however composite 3D auxetic structures are rarely reported. Auxetic structures are normally of low stiffness which causes limitations on the structural applications of them. The specific stiffness and strength of auxetic structures can be significantly improved by making them from high-performance fibre reinforced polymer (FRP) composites. Consequently, research of composite 3D auxetic structures made from FRP should be conducted. This paper presents the composite 3D double-arrow-head (DAH) auxetic structure made from carbon fibre reinforced polymer (CFRP) using an assembly method. Experimental, finite element and theoretical methods are adopted to study the mechanical properties of the composite 3D DAH auxetic structures. Results show that the Poisson's ratios and effective compression moduli of the composite 3D DAH auxetic structures vary depending on the compression strain amplitude, and the structures become more auxetic and stiffer with the increase of the compression strain. The specific stiffness of the composite 3D DAH structure is much higher than that of the metal structure. In addition, the dependences of the structure's Poisson's ratio and effective compression modulus on the geometry parameters have also been given. Making auxetic structures from high-performance FRP composites can significantly improve their mechanical properties which will enable them to have a much wider variety of applications.