In this study, numerical solution of non-Fourier heat conduction is discussed by a fractional single phase lag model in an inhomogeneous hollow cylinder made of a functionally graded material. For this purpose, all material properties of the media are assumed to vary continuously according to a power-law formulation except the phase lag and fractional order considered as constants. It is assumed that the cylinder is one-dimensional, symmetric and without any heat source. The governing equation has been solved numerically in a try and error algorithm to find the phase lag and the fractional order using an implicit numerical method. In order to validate the results, the numerical solutions of the fractional single phase lag model and the dual phase lag model are compared to the results of semi-analytical dual-phase lag. In the following the influence of non-homogeneity parameters is studied on the maximum transient temperature and thermal wave transmission speed. The temperature distribution is investigated from wave creation instance to steady state thermal distribution. Finally, the effect of different time delays and fraction orders on the temperature distribution is investigated.