We provide a detailed study of the leakage tunneling current through two cascaded-barrier structures with different; potentials sandwiched between a metal and substrate electrodes. The current-voltage (I-V) characteristics were obtained by solving the time-dependent Schrodinger equation. The structure Al/Ta2O5/SiO2/n(+)-Si is taken as an example. The effects of the SiO2 barrier thickness and the gate biasing polarity are studied. We found that the effect of the SiO2 barrier thickness, along with positive gale biasing was to slightly reduce the leakage current value. However, the effect of the SiO2 layer thickness, along with negative gate biasing, was to significantly change the I-V characteristics. The computed I-V characteristics were plotted according to the Fowler-Nordheim tunneling expression to check on its adequacy for cascaded potentials. Such plots will also be valuable in evaluating experimental findings. Results are compared with recently published experimental results on Ta2O5 thin films on Si substrates.