It has recently been demonstrated that superatoms, which can exhibit behaviors reminiscent of atoms in the periodic table, might have synthetic utility, and represent potential building blocks for the assembly of novel, nanostructured materials [Science 2004, 304, 84-87; Science 2005, 307, 231-235; J. Phys. Chem. C 2009, 113, 2664]. In this work, a new type of endohedral metallofullerene-superhalogen compound, Li@C60-BX4 (X = F, Cl, Br), is proposed and characterized using density functional theory. The electron transfer from Li@C60 to BX4 contributes greatly to the Li@C60-BX4 compound formation. Such compounds exhibit considerable stabilities with large binding energies and ionization potentials, as well as large HOMO-LUMO gaps. The investigation of the nonlinear optical (NLO) properties of Li@C60-BX4 reveals a strong dependence of the static first hyperpolarizability, β0, on the atomic number of the involved halogen atom X. This means that one can enhance the first hyperpolarizabilities of the endohedral metallofullerene by introducing superhalogens. The present investigation may promote the development of novel nanomaterials with unusual properties (i.e. NLO properties), and enrich the knowledge of chemical bonds (for example, long-range interactions between trapped atoms in a C60 cage and the outside superatom motif).