The transport properties and differential conductance of the heterostructures constructed by (5,5) single wall carbon nanotube (SWCNT) and (5,5) single wall boron nitride nanotube (SWBNNT) are investigated using density functional theory in combination with non-equilibrium Green's functions. We find that the transmission conductance of (5,5) BN/C nanotube heterostructure is not only continually depressed as the BNNT region increases but also the drop of the conductance is uniform in the energy window (-1.43 eV, 1 eV), which leads to linear I-V dependence for the systems when the bias is within this energy range. Moreover, the differential conductance linearly decreases when n ≤ 3 but exponentially decreases when n ≥ 3 for (5,5)(BN) n /C heterostructure. Such tunable differential conductance of (5,5) BN/C nanotube heterostructure mainly derives from the blockage of the transport channels induced by the semiconductive BN segment.