Is the parrot colored? And by colored, I mean that it's red/orange or yellow? If it's still gray (juvenile), the line is normal. If it is colored, the other fish could be chasing him, stressing him out. Do a water change and at the same time add a couple extra hiding places and rearrange the decor. Depending on the size of your other fish in comparison to the parrots, he is probably being bullied. Some Blood Parrots are actually born with the black stripes or splotching. It's not as common, but it happens. If it's just a single straight line across the top of his body, it's stress. The water change will help and so will the extra hiding places. You may even want to add some more greenery.
About 8 months ago our little yellow parrot got a black line so we added 2 pieces of tall greenery, a cave, did a water change, and within a couple hours it was starting to fade, but it took about a week for it to completely disappear. When you bought him did he have a black stripe on him?