Well, yes, in my opinion, black background in the text is good for your eyes. Generally speaking, when you use the black background, it will be suitable for view both during bright day and dark night. And that will not lead to eye strain, and make your eyes tired. But on the other hand, if you choose white background, it will be painful to view at night. So I will suggest you choose black background.
It is said that the light brown, light yellow, yellow green and light green color are the good background for the eyes in the text. The black color is so dark which will cause the eyes to be easily in tiredness. The white background is too bright which is also not the best choice. You could choose the above colors to make your eyes feel comfortable when seeing.
As from as I know, the darker the background is, the less harm your eyes will receive, it is a principle that I learned from my life experience. Just try not to get white or red background, which could make your eyes fatigue within less time. You should also try to take some breaks at intervals to better protect your eyes and vision. More vitamins are also effective.