How do I remove black background from a vector graphic?

If you Expand the Image Trace object, it's easy to fix.

1. Select the object and you'll see an Expand button in the Control panel, or in the new Properties panel.
2. Switch to your Direct Selection tool (A), and deselect all by clicking off to the expanded object.
3. Click on one of the shapes that's filled with the color your wish to delete.
4. Under the Select meant, choose Same > Fill Color.
5. Press Delete.

If you wish to delete just a white or black background, click on just that shape with the Direct Selection tool and delete.

PalavenLost, themcalghamdi,

As I (mis)understand it, you (both) have an actual background object, whether vector artwork or raster image, and you can simply hide it or delete it (preferably doing it on a duplicate Layer).

PalavenLost, for a logo you may wish to redraw rather than Image Trace.

I have same problem...

how to take this black background...

should be like this...

Yes illustrator by default has a transparent background. The white canvas is just there to be a less annoying view and what is preferred by most users.

Use Shift Command D to toggle the view. The checkerboard pattern denotes what is transparent.

If you have any more questions, can you please include a screenshot so we can better understand/decipher/discuss what you asking.