<p>The indentation response of rigid flat indenters on a transversely isotropic (TI) functionally graded (FG) thin film is of great significance in many engineering fields. Multi-layer structures are often employed to approximate FG materials; however, this approach, together with the low computational efficiency in the accurately self-adaptive semi-infinite integration algorithm, has led to high computational costs in previous analyses. To address these limitations, we develop an indentation response model for a flat indenter acting on an FG thin film bonded to a homogeneous substrate with an imperfect interface. The model employs the novel Fourier–Bessel series (FBS) system of vector functions to derive the Green’s function solution, in which the field quantities are expanded as discrete Love numbers, enabling accurate results through simple summation. The resulting Green’s function is then combined with a boundary discretization scheme to obtain the indentation response. The developed model is first validated against existing solutions for a flat indenter on a transversely isotropic elastic half-space. The superior computational efficiency of the present study is demonstrated by comparison with the previous benchmark solution. Parametric studies are subsequently carried out to examine the influence of the gradient index and interface imperfections on the indentation response. Results demonstrate that the thin-film material properties and the degree of interface imperfection are decisive in governing the indentation behavior. The proposed model offers valuable insights for the design and optimization of the FG thin-film.</p>