Warm(- 10E4 K), low-density(- 0.1 cm-3) ionized gas is widespread over the whole sky with a typical Galactic scale height of 1 Kpc, producing the optical H_alpha background (Reynolds 1992). The source of ionization is not yet clear, and furthermore, the relationship between the warm ionized medium and other interstellar medium such as HI clouds and the hot ionized coronal gas, is not understood yet. As for the source of the ionization, probably photoionization by UV photons may not explain fully the properties of the warm ionized medium observed at optical, and other mechanism, such as ionization by low velocity shocks, should be considered. In order to clarify the ionization mechanism and to study the origin of the diffuse warm ionized medium, we propose far-infrared spectroscopic observations using the LWS toward several targets selected from the H_alpha map by Reynolds(1992). In the far-infrared, there are also many spectral lines as in optical which can be used as diagnostic tools of physical condition of the matter. Moreover, observation from space does not suffer from contamination by terrestrial emission, while ground-based optical observation sometimes suffers. Part of the observation will be executed in the Japanese guaranteed time, and this proposed observation greatly supplements the guaranteed time observations.