We present observational results from optical long-slit spectroscopy of parsec-scale jets of DG Tau. From HH 158 and HH 702, the optical emission lines of H, [O i] 6300, 6363, [N ii] 6548, 6584, and [S ii] 6716, 6731 are obtained. The kinematics and physical properties (i.e., electron density, electron temperature, ionization fraction, and mass-loss rate) are investigated along the blueshifted jet up to 650′′ distance from the source. For HH 158, the radial velocity ranges from -50 to -250 km s-1. The proper motion of the knots is 0:′′196 - 0:′′272 yr-1. The electron density is 104 cm-3 close to the star, and decreases to 102 cm-3 at 14′′ away from the star. Ionization fraction indicates that the gas is almost neutral in the vicinity of the source. It increases up to over 0.4 along the distance. HH 702 is located at 650′′ from the source. It shows  -80 km s-1 in the radial velocity. Its line ratios are similar to those at knot C of HH 158. The mass-loss rate is estimated to be about  10-7 M⊙ yr-1, which is similar to values obtained from previous studies.