  We develop a magnetohydrodynamical model of Alfv\'en wave-driven wind in open
magnetic flux tubes piercing the stellar surface of Red Giant Branch (RGB) and
Asymptotic Giant Branch (AGB) stars, and investigate the physical properties of
the winds. The model simulations are carried out along the evolutionary tracks
of stars with initial mass in the range of 1.5 to 3.0 $M_{\odot}$ and initial
metallicity $Z_{\rm ini}$=0.02. The surface magnetic field strength being set
to be 1G, we find that the wind during the evolution of star can be classified
into the following four types; the first is the wind with the velocity higher
than 80 km s$^{-1}$ in the RGB and early AGB (E-AGB) phases; the second is the
wind with outflow velocity less than 10 km s$^{-1}$ seen around the tip of RGB
or in the E-AGB phase; the third is the unstable wind in the E-AGB and
thermally pulsing AGB (TP-AGB) phases; the fourth is the stable massive and
slow wind with the mass-loss rate higher than 10$^{-7} M_{\odot}$ yr$^{-1}$ and
the outflow velocity lower than 20 km s$^{-1}$ in the TP-AGB phase. The
mass-loss rates in the first and second types of wind are two or three orders
of magnitude lower than the values evaluated by an empirical formula. The
presence of massive and slow wind of the fourth type suggests the possibility
that the massive outflow observed in TP-AGB stars could be attributed to the
Alfv\'en wave-driven wind.
