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 $aga 10^{-6}$ cm. We also show that shattering in warm neutral medium (WNM) can limit the largest grain size in ISM ($asim 2times 10^{-5} mathrm{cm}$). 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.
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