In this paper, some nonlinear Lane-Emden type equations arising in astrophysics are solved by Chebyshev Finite Difference Method. Convergence and error analysis of the method are examined. To show the applicability and efficiency, some astrophysics problems such as the isothermal gas spheres, standard Lane-Emden equation and white-dwarf equation are realized. Besides, the method carried out for some boundary value problems, and it is shown that the method also works with boundary conditions as well as with initial conditions without any modification. The results demonstrated that the proposed method is rather efficient and more accurate than the many methods given in the literature.