We studied the electrical properties of silicon nanocrystals (Si-ncs) with a wide size distribution embedded in an oxide matrix. A wide Coulomb gap, clear current bumps, and significant current oscillations and jumps were observed at room temperature in the current vs. voltage characteristics of an Al/silicon-rich oxide/Si MOS-like structure. These anomalies can be well explained by quantum tunneling and Coulomb blockade effects. High-frequency capacitance vs. voltage, and conductance vs. voltage curves show jumps in similar voltage range supporting this explanation. The fact that the charging energy due to the Coulomb blockade effect is much larger than the quantum level spacing weakens the strict size-dependence of the quantum tunneling. The high density of Si-ncs in the oxide layer also enables the carriers to always find Si-ncs of similar size close enough to tunnel through.