The DFT cluster method was employed to investigate the electronic structures and muonium hyperfine interactions in guanine nucleobase and nucleotide using three different basis sets. The total energy and Fermi contact values were calculated for muon trapped at carbon '8'. The three basis sets, 6-31G, 6-311G and 6-311G(d,p), were used in tandem with the B3LYP functional. There are significant quantitative differences in the calculated total energy. 6-311G(d,p) produced the lowest total energy as compared to the other basis sets. The lowering of the total energy is due to the increase in the number of basis functions to describe the atomic orbitals, which is consistent with the postulate on basis set completeness. The 6-31G basis set produced the muon Fermi contact value that is the closest to the experimental value. The calculated Fermi contact values for the nucleobase and nucleotide are significantly lowered in going from the double-zeta to the triple-zeta basis set by 5% and 4% respectively. The lowering of the Fermi contact value can be attributed to the extension of the triple-zeta basis set in describing the valence atomic orbitals. The presence of the sugar phosphate group in the nucleotide instead of the methyl group tends to lower the Fermi contact value. Thus, the sugar phosphate group should be taken into consideration when designing a calculation model.