Single-walled carbon nanotube (SWCNT) is a promising candidate for strengthening nanocomposite. As the matrix of nanocomposite, a single crystal of copper is designed to be in-plane auxetic along the crystal orientation [1 1 0]. In that way, the nanocomposite could also be auxetic when enhanced by (7, 2) a single-walled carbon nanotube with relatively small in-plane Poisson’s ratio. A series of molecular dynamics (MD) models of the nanocomposite metamaterial are then established to study mechanical behaviors of the nanocomposite. In the modelling, the gap between copper and SWCNT is determined following the principle of crystal stability. The enhanced effect for different content and temperature in different directions is discussed in detail. This study provides a complete set of mechanical parameters of nanocomposite including thermal expansion coefficients (TECs) from 300 K to 800 K for five weight fractions, which is essential for a wide range of applications of auxetic nanocomposites in the future.