The Lane-Emden type equations are employed in the modeling of several phenomena in the areas of mathematical physics and astrophysics. These equations are categorized as non-linear singular ordinary differential equations on the semi-infinite domain. In this paper, the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) of the first kind have been introduced as a new basis for Spectral methods, and also presented an effective numerical method based on the GFCFs and the collocation method for solving the nonlinear singular Lane-Emden type equations of various orders. Obtained results have compared with other results to verify the accuracy and efficiency of the presented method.