Observed reddening in the circum-galactic medium (CGM) indicates a significant abundance of small grains, of which the origin is still to be clarified. We examine a possible path of small-grain production through shattering of pre-existing large grains in the CGM. Possible sites where shattering occurs on a reasonable time-scale are cool clumps with hydrogen number density $n_mathrm{H}sim 0.1$ cm$^{-3}$ and gas temperature $T_mathrm{gas}sim 10^4$ K, which are shown to exist through observations of Mg II absorbers. We calculate the evolution of grain size distribution in physical conditions appropriate for cool clumps in the CGM, starting from a large-grain-dominated distribution suggested from theoretical studies. With an appropriate gas turbulence model expected from the physical condition of cold clumps (maximum eddy size and velocity of $sim$100 pc and 10 km s$^{-1}$, respectively), together with the above gas density and temperature and the dust-to-gas mass ratio inferred from observations (0.006), we find that small-grain production occurs on a time-scale (a few $times 10^8$ yr) comparable to the lifetime of cool clumps derived in the literature. Thus, the physical conditions of the cool clouds are favrourable for small-grain production. We also confirm that the reddening becomes significant on the above time-scale. Therefore, we conclude that small-grain production by shattering is a probable cause for the observed reddening in the CGM. We also mention the effect of grain materials (or their mixtures) on the reddening at different redshifts (1 and 2).
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