Structure and molecular first hyperpolarizability (β) of nitro-amino-substituted 6-vertex 1,6-carboranes are investigated by means of DFT calculations. The results obtained have revealed that the relative orientation of substituents with respect to the carborane cage influences bond lengths distribution in the cage, which leads to significant changes in the values of hyperpolarizabilities. Calculations with different basis sets have demonstrated that the value of β is not significantly affected by the choice of basis set. The calculated data shows that hyperpolarizability of carborane molecules substituted for carbon atoms is lower than when substituted for boron atoms. For latter molecule, the value of β is of the same order as that of para-nitroaniline molecule.