Lyman-break galaxies ( LBGs ) contain a non-negligible amount of dust . Takeuchi et al . ( 2003a ) ( T03 ) constructed a model of the infrared spectral energy distribution ( SED ) for very young galaxies by taking into account the dust size distribution in the early stage of galaxy evolution , which can be different from that of present-day evolved galaxies . We applied T03 model to LBGs and constructed their expected SED . In order to examine the grain size distribution of dust , we calculated the SEDs based on two distinct type of the distribution models : a single-sized distribution and a power-law distribution with a slope of dN / da \propto a ^ { -3.5 } . We found that the single-sized and power-law dust size distributions yield a very similar detectability of LBGs at the submillimetre ( submm ) . We also found that galaxies with a power-law dust distribution have much less flux at mid-infrared ( MIR ) than the other . By making use of this fact we can explore the dust grain size distribution in high-redshift galaxies through ( observer-frame ) FIR observations . Then , we applied the model to a gravitationally lensed LBG MS 1512 - cB58 ( cB58 ) , a unique probe of the dust emission from LBGs . Observations by SCUBA suggest that the dust is hot in this galaxy . Our model framework well reproduced the hot dust temperature under a natural assumption for this galaxy . We also examined the detectability of LBGs at submm wavelengths in an eight-hour deep survey by ALMA . The LBG population with an age \ga 10 ^ { 8 } { yr } and a SFR \ga 10 M _ { \odot } { yr } ^ { -1 } can be detected in such a survey . By integrating over their redshifted SEDs with the observed luminosity functions , we obtained the contribution of LBGs to the cosmic infrared background radiation ( CIRB ) . Although they have non-negligible amount of dust , their contribution was found to be small , especially in the FIR \sim 200 \mu m. Thus , we need a strongly obscured population of galaxies which contains a large amount of star formation , at some epoch in the history of the universe .