The initial stage of hydrogen (H) adsorption on the Si(001) surface is theoretically investigated to clarify the atomic and electronic structure induced by the adsorption. For this purpose, the electronic states are calculated in the density functional approach with the DV(discretized variation)-Xα-LCAO method. We also simulate the scanning tunneling microscopy (STM) image and the scanning tunneling spectroscopy (STS) spectrum in the first-principles approach. Our results of the STM image do not support the asymmetric dimer structure of the substrate with a H atom bonded to the upper Si atom. They conclude that the bright ball-like spot in the observed images comes from the free dangling bond induced on the remaining Si atom of the reacted dimer. However, the single particle picture cannot reproduce the observed features of the STS spectrum at the spot. We discuss that all the features can be well explained by the Coulomb blockade effect due to the electron correlation in the dangling bond state.