There are two completely different points to consider here.
First of all, as far as I can see you are looking at a perfectly periodic (14,0) nanotube. In such as system, under elastic and coherent condition (which is what ATK considers) there is no scattering, and thus no potential drop. Therefore, you cannot really apply a finite bias across the structure. You can try, of course, but the risk is that the calculation doesn't converge, and if it does, the results are pretty uninteresting anyway.
Now, there is a totally separate issue with your results - you have a negative current for positive bias, and this can only occur if the transmission spectrum is negative, which is not physical. This can occur numerically though, either as a result of the problems described above (bad convergence) or as a numerical artifact which can produce very small negative transmission values (-1e-10 or so). This gives a negative current, but a very small one. Indeed, you report nA, which is quite tiny, and this is of course not surprising since you have a (14,0) nanotube where the band gap should be close to 0.8 eV, and so no current should flow until you apply at least that amount of bias, which seems to be where your current takes off, so that's consistent at least.
So, all in all, I would suspect, perhaps, that your low-bias current is due to numerical issues; you can check this by plotting the transmission spectrum, and look for small negative values. However, and this is key, even if you get a more "correct" plot, to study a perfectly periodic system with an applied bias does not produce any scientifically valuable results - and also there is no point really in doing an advanced transport calculation, since you can just get the I-V curve from extrapolating the zero-bias transmission (which can be computed from the bulk structure). But really you need to introduce scattering to have an interesting problem to study.
