This study aims to investigate the elastic response of a two-dimensional, surface-loaded substrate coated by a multi-layered system consisting of one-dimensional hexagonal quasicrystal materials. A linear elasticity theory for quasicrystals is adopted to simulate phonon and phason elastic fields. First, a set of governing differential equations for each layer is established in terms of the phonon and phason displacements. The general solution for a generic layer is constructed through the Fourier transform method in a closed form in the transform space. This solution is then utilized to formulate a layer stiffness equation. Adopting a direct stiffness method along with continuity along the layer interfaces, a stiffness equation for the multi-layered coated substrate is derived. An efficient quadrature is adopted to evaluate all involved integrals resulting from Fourier integral inversion. After verification with benchmark cases, the capability of the derived solutions are demonstrated by investigating the influence of various parameters such as layer thickness, layer arrangement, and loading conditions on the predicted response. Finally, applications of the developed multi-layer scheme to tackle a functionally graded quasicrystal layer are elucidated.