Solving numerically the time-dependent Schrödinger equation in three-dimensional momentum space, we have investigated the energy spectroscopy and two-dimensional momentum angular distribution near the ionization threshold of the photoelectron generated from excited atom under the action of high-frequency laser pulse. The results show that the ionized process is mainly the single-photon ionization in this energy range. The principal quantum number of the initial state can be determined by the position of the first peak in photoelectron spectrum; its angular quantum number of the initial state can be determined by the angular distribution of the two-dimensional momentum of the photoelectron. This law does not change with the variation of the intensity and pulse duration of the incident laser pulse within a relatively broad range of these parameters. In principle, we can utilize these spectra to identify the initial state of the atoms. In addition, the photoelectron momentum spectrum of superposition state is investigated for different relative phase of the state.