A series of Li-corannulene-(NH2)n and Li-corannulene-(NO2)n (n = 1, 2, 5) compounds have been theoretically designed and investigated using density functional theory. In this work, two models are systematically investigated to explore the important factors for enhancing the static first hyperpolarizability by introducing the substitution group. It is revealed that energy gaps (Egap) between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of all compounds are in the range of 4.149-4.934 eV. Different DFT methods are adopted to calculate polarizabilities and the first hyperpolarizabilities of Li-corannulene-(NH2)n and Li-corannulene-(NO2)n (n = 1, 2, 5) compounds. It is revealed that polarizability values of the systems increase with increasing number of NH2/NO2 substitution group. Moreover, it is found that the first hyperpolarizabilities of Li-corannulene-(NO2)n are larger than those of Li-corannulene-(NH2)n, which can be attributed to the lower transition energies. In contrast to the NH2 substitution group, NO2 substitution group can be more powerful in increasing the first hyperpolarizability of Li-doped corannulene. We hope that this study can provide a new idea for designing nonlinear optical materials using the NH2 and NO2 groups.