  We investigate shattering and coagulation of dust grains in turbulent
interstellar medium (ISM). The typical velocity of dust grain as a function of
grain size has been calculated for various ISM phases based on a theory of
grain dynamics in compressible magnetohydrodynamic turbulence. In this paper,
we develop a scheme of grain shattering and coagulation and apply it to
turbulent ISM by using the grain velocities predicted by the above turbulence
theory. Since large grains tend to acquire large velocity dispersions as shown
by earlier studies, large grains tend to be shattered. Large shattering effects
are indeed seen in warm ionized medium (WIM) within a few Myr for grains with
radius $a\ga 10^{-6}$ cm. We also show that shattering in warm neutral medium
(WNM) can limit the largest grain size in ISM ($a\sim 2\times 10^{-5}
\mathrm{cm}$). On the other hand, coagulation tends to modify small grains
since it only occurs when the grain velocity is small enough. Coagulation
significantly modifies the grain size distribution in dense clouds (DC), where
a large fraction of the grains with $a<10^{-6}$ cm coagulate in 10 Myr. In
fact, the correlation among $R_V$, the carbon bump strength, and the
ultraviolet slope in the observed Milky Way extinction curves can be explained
by the coagulation in DC. It is possible that the grain size distribution in
the Milky Way is determined by a combination of all the above effects of
shattering and coagulation. Considering that shattering and coagulation in
turbulence are effective if dust-to-gas ratio is typically more than $\sim
1/10$ of the Galactic value, the regulation mechanism of grain size
distribution should be different between metal-poor and metal-rich
environments.
