DG Tau is a classical T Tauri star with a fast collimated jet and protoplanetary disk winds. Although the jet is relatively well studied, there are still many unknowns regarding the winds. From previous studies, the low-velocity components (LVC, v<100 km s-1) in the forbidden line profiles have been used as a proxy for the winds. We aim to study the properties of the LVC and illustrate the structure of the winds that potentially affects disk dispersal. Using Subaru-HDS, we obtained high spectral resolution spectra (Δv ~ 2.5 km/s) and detected 22 optical forbidden lines from DG Tau. LVCs were found in [O I] (5577/6300/6363 Å), [S II] (6716/6731 Å), [N I] 5200 Å, and possibly [Fe II] 5527 Å. We measure their angular scales of 0”.05-0”.4 (10-60 au) using spectro-astrometry. In addition, high-velocity components (HVC) associated with the collimated jet were found in 20 lines ([N I], [N II], [O I], [O III], [S II], [Ca II], [Fe II]). Our analysis reveals that the HVCs have a higher temperature and a lower density toward the downstream and traces a fast collimated jet. The LVCs also show the same trends and can be divided into three sub-components: LVC-H, LVC-M, and LVC-L. Within these LVC components, LVC-H may trace turbulent gas surrounding the jet, while LVC-M and -L may trace slower wide-angled components close to the star.