A molecular memory device which has a structure of Al/$Al_2O_3$/ASA-15 LB monolayer/Ti/Al device, was fabricated. To study a charge transfer mechanism of molecular memory devices, current density-voltage (J-V) characteristics were measured at an increasing temperature range from 10 K to 300 K with an interval of 30 K. Strong temperature-dependent electrical property and tunneling through organic monolayer at low bias (below 0.5 V) were appeared. These experimental data were fitted by using a theoretical formula such as the Simmons model. In comparison between the theoretical and the experimental results, it was verified that the fitting results using the Simmons model about direct tunneling was fairly fitted below 0.5 V at both 300 K and 10 K. Hopping conduction was also dominant at all voltage range above 200 K due to charges trapped by defects located within the dielectric stack, including the $Al_2O_3$, organic monolayer and Ti interfaces.