The tunneling current flowing between the tip and H-adsorbed Si(001) surface in Scanning Tunneling Microscopy (STM) is investigated using the first-principles calculations based on the real-space finite-difference method. The resultant current map is consistent with the STM image in which H-adsorbed dimer looks geometrically lower than the bare dimer. Although the isosurface of the local density of states above the H-terminated Si dimer, which are mainly attributed by the Si-H σ bonding states, locate itself higher than that above the bare Si buckled dimer, these bonding states do not contribute to the tunneling current. On the other hand, many electrons tunnel from π bond of the unreacted dimer into the tip. Accordingly, the H-adsorbed dimer appears geometrically lower than the bare dimer in the STM, since the tip must approach closer to the sample surface in order to achieve the constant tunneling current.