We report an observation of the Draco cloud region using the Far-ultraviolet IMaging Spectrograph (FIMS/SPEAR). The spectra show important ionic lines, such as CIV lambda lambda 1548, 1551, Si IV+OIV] lambda 1394, Si II* lambda 1533, and Al II lambda 1671, indicating the existence of hot and warm interstellar gases toward the region. The map of the continuum is generally in accord with the infrared map, which indicates far-ultraviolet continuum is mostly the starlight scattered off by the dust grains in the Draco cloud. Enhanced C IV emission is seen inside the Draco cloud region and attributed to the turbulent mixing of the interacting cold and warm/hot media. This interpretation is supported by the detection of O III] lambda 1661 emission line and the Ha feature in this region. We found slightly fainter C IV and far brighter Si II* emissions covering the rest of the region outside the Draco cloud, in agreement with previous observations of Galactic halos. Additionally, we also found that the molecular hydrogen fluorescence map is consistent with the morphology of the atomic neutral hydrogen and dust emission of the Draco cloud, direct evidence supporting the notion that substantial amounts of hydrogen nuclei exist in molecular form in the cloud.