The effects of various buffer layers on the InN growth were studied by using atomic force microscopy (AFM), X-ray diffraction (XRD), KOH wet etching and photoluminescence (PL). GaN or InN buffers with various temperatures and conditions were prepared for the InN growth by using plasma-assisted molecular beam epitaxy (PAMBE). For GaN buffers, the InN polarity was controlled by the GaN polarity. Namely, high temperature buffers (HT, 765°C-880°C) led to -c polar InN with better quality, while intermediate-temperature buffers (IT, 500°C-650°C) to +c polar InN with lower quality. When InN buffer was used, the quality of main InN was lower than that on GaN buffer. This reason is attributed to the twist misorientation (rotation of InN unit cell along c-axis) in InN/InN-buffer/sapphire structure. This drawback has been effectively suppressed by a longer substrate nitridation, or by inserting a GaN buffer between sapphire and InN buffer. By comparing the InN grown on GaN, InN or (GaN + InN) buffer, we concluded that GaN grown at about 800°C was the optimal buffer because it had atomically flat surface and led to -c polar InN with small misorientation.