In the recent years, growing interest in dust charging physics is connected with several lander missions running on or planned to the Moon, Mars, and Mercury for a near future. In support of these missions, laboratory simulations are a potential tool to optimize in situ exploration and measurements. In the paper, we have investigated electrical properties of a Martian soil simulant prepared at the Johnson Space Center under name JSC Mars-1 using the dust charging experiment when a single dust grain is trapped in a vacuum chamber and its secondary electron emission is studied. The exposure of the grain to the electron beam revealed that the grain surface potential is low and generally determined by a mean atomic number of the grain material at a low-energy range (<1 keV), whereas it can reach a limit of the field ion emission being irradiated by more energetic electrons. A comparison of model and experimental results reveals an influence of the grain shape and size predominantly in the range of higher (>2 keV) electron energies. We discuss possible implications of the secondary electron emission for the presence of lightnings on Mars.