This work develops a multi-objective design optimisation method for Carbon Nanotube Composite Structures (CNTCSs) using Genetic Algorithm and Finite Element Analysis (FEA). Two design problems are considered: the first is an optimisation problem to improve the mechanical properties (weight-displacement) of the CNTCSs, minimizing the Not Adherence Green Design Principles (NoAGDP); the second is an optimisation problem to improve the same mechanical properties also minimizing the cost of the CNTCSs. Numerical results show in both cases that a set of optimal CNTCSs can be found, which has similar stiffness, weight and NoAGDP, with sensitive cost increments, compared to common polymer structures.