In the present paper, carbon nanotube (CNT) reinforced functionally graded (FG) material matrix nanocomposite (CNT-FGM) is indented with a rigid conical indenter and the contact behaviour of the CNT-FGM nanocomposite is analyzed in the context of variation in gradation parameter and wall thickness of the CNTs. The study is conducted on the basis of finite element model, which is developed utilizing Ansys Parametric Design Language (APDL) codes in commercial finite element modelling platform, ANSYS. The material model is developed considering the CNTs are uniformly distributed in the graded matrix, whose elastic properties vary along the direction of indentation. The gradation model, corresponding to the matrix material, adopted for the present study is a power law function. In this study, elastically graded material (EGM)matrix CNT reinforced CNT-FGM nanocomposite has been examined, varying the elastic gradation parameter (+2, 0 and -2) of the matrix material. Additionally, effect of the variations in CNT wall thickness are explored, while maintaining other parameter constant in the nanocomposite. A frictionless contact between the CNT-FGM substrate and rigid indenter is simulated for both loading and unloading process. Prior to extracting pertinent results, the current model undergoes validation by comparing its outcomes with those published in the literature. It is observed that the contact force-displacement plots align satisfactorily for both sets of data. Various contact parameters, such as contact force, contact area, contact pressure distribution, stress distribution, and deformation behavior during the indentation contact, are then extracted from the analysis. The observation indicates that positive gradation parameter result in superior contact properties compared to negative gradation parameters as well as without gradation.