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In this article, we introduce a fractional order of rational Bessel functions collocation method (FRBC) for solving the Thomas-Fermi equation. The problem is defined in the semi-infinite domain and has a singularity at x = 0 and its boundary condition occurs at infinity. We solve the problem on the semi-infinite domain without any domain truncation or transformation of the domain of the problem to a finite domain. This approach at first, obtains a sequence of linear differential equations by using the quasilinearization method (QLM), then at each iteration the equation is solves by FRBC method. To illustrate the reliability of this work, we compare the numerical results of the present method with some well-known results, to show that the new method is accurate, efficient and applicable. [ABSTRACT FROM AUTHOR]