  We use large cosmological Smoothed-Particle-Hydrodynamics simulations to
study the formation and evolution of sub-millimetre galaxies (SMGs). In our
previous work, we studied the statistical properties of ultra-violet selected
star-forming galaxies at high redshifts. We populate the same cosmological
simulations with SMGs by calculating the reprocess of stellar light by dust
grains into far-infrared to millimetre wavebands in a self-consistent manner.
We generate light-cone outputs to compare directly the statistical properties
of the simulated SMGs with available observations. Our model reproduces the
submm source number counts and the clustering amplitude. We show that bright
SMGs with flux $S > 1$ mJy reside in halos with mass of $\sim 10^{13}
M_{\odot}$ and have stellar masses greater than $10^{11}\sim \rm M_{\odot}$.
The angular cross-correlation between the SMGs and Lyman-$\alpha$ emitters is
significantly weaker than that between the SMGs and Lyman-break galaxies. The
cross-correlation is also weaker than the auto-correlation of the SMGs. The
redshift distribution of the SMGs shows a broad peak at $z \sim 2$, where
Bright SMGs contribute significantly to the global cosmic star formation rate
density. Our model predicts that there are hundreds of SMGs with $S > 0.1$ mJy
at $z > 5$ per 1 square degree field. Such SMGs can be detected by ALMA.
