Non-equilibrium Green's functions (NEGF) formalism combined with extended Hückel (EHT) and charging model are used to study electrical conduction through single-molecule junctions. The analyzed molecular complex is composed of the asymmetric 1,4-Bis((2′-para-mercaptophenyl)-ethinyl)-2-acetyl-amino-5-nitrobenzene molecule symmetrically coupled to two gold electrodes. Owing to this model, the accurate values of the current flowing through such junctions can be obtained by utilizing basic fundamentals and coherently deriving model parameters. Furthermore, the influence of the charging effect on the transport characteristics is emphasized. In particular, charging-induced reduction of conductance gap, charging-induced rectification effect and charging-generated negative value of the second derivative of the current with respect to voltage are observed and examined for the molecular complex.