The Owl Nebula (NGC 3587) is a double shell nebula. An additional faint halo is recently found in interference filter CCD images (Kwitter, Chu, & Downes 1992, in IAU Symp. 155). To confirm and to determine the physical nature of this halo, we have obtained spectra of the Owl Nebula with the IDS spectrograph on the INT 2.5m telescope at La Palma. The spectra covered emission lines of Hα , Hβ , Hγ , [O III], HeI, [N II], and [S II]. The instrumental FWHM is 23+/-2 km s(-1) . We were able to measure not only the line ratios but also kinematics in the nebula. Both the main nebula and the faint halo of the Owl Nebula were detected in our spectroscopic observations. The halo has distinctly different physical properties from the main nebula. The main nebula seems to be an hollow expanding shell; the double-shell structure seen in the direct images does not show any differences in kinematics. The expansion velocity of the main nebula is measured to be 28, 27, 37, and 39 km s(-1) in the Hα , [O III], [S II], and [N II] lines, respectively. The halo, on the other hand, shows an observed line width close to the instrumental width, indicating an expansion velocity <<10 km s(-1) . The halo is kinematically independent from the main nebula. The relative line strengths in the halo are also different from those in the main nebula. Most notably, the [N II]/Hα ratio of the halo is a factor of 4 higher than that of the inner part of the main nebula. This indicates that the halo is photoionized. A lower limit of the dynamic age of the halo can be calculated from its size and the upper limit on its expansion velocity. At an adopted distance of 430 pc, the halo radius would be 0.4 pc and the dynamic age is >40,000 yr, while the inner nebula has a dynamic age of 8,000 yr. These timescales indicate that the main nebula consists of superwind from the AGB phase and the faint halo consists of the earlier red giant wind from a 1--2 M_sun star.