Scanning tunneling spectroscopy in the shell-filling regime was carried out at room temperature to investigate the size dependence of the band gap and single-electron charging energy of single Si quantum dots (QDs). The results are compared with model calculation. A 12-fold multiple staircase structure was observed for a QD of about 4.3 nm diameter, reflecting the degeneracy of the first energy level, as expected from theoretical calculations. The systematic broadening of the tunneling spectroscopy peaks with decreasing dot diameter is attributed to the reduced barrier height for smaller dot sizes and to the splitting of the first energy level.