We have succeeded in achieving high-quality thin InN films (<500 nm) by low-plasma-power growth. In this study, we investigated the thickness dependence of the structural and electrical properties of relatively thin InN films grown by radio-frequency plasma-assisted molecular beam epitaxy (RF-MBE). InN films were grown by RF-MBE on GaN/sapphire templates at 80 W, which is lower than that for conventional InN growth (200 W). The films had thicknesses of 5, 20, 100, 200, and 460 nm. The mobility and carrier concentration of InN degraded with decreasing InN film thickness, although even 200-nm-thick InN demonstrated relatively good characteristics (mu = 1540 cm(2) V-1 s(-1) and n = 2.1 x 10(18) cm(-3)). On the other hand, the FWHM values of the (002) and (302) X-ray rocking curves (XRCs) were minimum in 5-nm-thick InN and increased with film thickness up to approximately 100-200 nm. This seems to be due to the formation of small grains with better crystal quality at the initial stage. It is also suggested that these grain structures with poor coalescence and roughness caused the deterioration of InN electronic properties in a very thin region. (C) 2013 The Japan Society of Applied Physics