Recent observations have indicated the existence of dust in high-redshift galaxies, however, the dust properties in them are still unknown. Here we present theoretical constraints on dust properties in Lyman-break galaxies (LBGs) at z = 3 by post-processing a cosmological smoothed particle hydrodynamics simulation with radiative transfer calculations. We calculate the dust extinction in 2800 dark matter haloes using the metallicity information of individual gas particles in our simulation. We use only bright galaxies with rest-frame ultraviolet (UV) magnitude M 1700 〈 –20 mag, and study the dust size, dust-to-metal mass ratio, and dust composition. From the comparison of calculated colour excess between B and V band [i.e. E ( B – V )] and the observations, we constrain the typical dust size, and show that the best-fitting dust grain size is ~ 0.05 μm, which is consistent with the results of theoretical dust models for Type II supernova. Our simulation with the dust extinction effect can naturally reproduce the observed rest-frame UV luminosity function of LBGs at z = 3 without assuming an ad hoc constant extinction value. In addition, in order to reproduce the observed mean E ( B – V ), we find that the dust-to-metal mass ratio needs to be similar to that of the local galaxies, and that the graphite dust is dominant or at least occupy half of dust mass.