We perform first-principles calculations to investigate the geometric and electronic properties of (10,0) and (5,5) BN/C nanotube heterostructures. We show that both of them have smooth interfaces which are free from bond mismatch and vacancy defect. Interface states appear in the band gaps, due to the discontinuity of π -π bonding of carbon nanotube segments, and exhibit asymmetric distribution in the two segments. The charge redistribution in the region near the interfaces gives rise to a build-in electric field and modulates the static electric potential profiles in the heterostructures. The band scheme diagrams of these heterostructures are also presented.