I'm trying to delete the background layer but I cannot select or right click to it.
I had been pasted a layer.
How can I fix this ? Thanks.
If you have pasted something that resulted in a temporary layer called "Floating selection", this can be your problem. While the "Floating selection" exists, many things are locked in Gimp. You have to get rid of the "Floating selection" by making it a true layer: use Layer>To new layer
or Ctrl-Shift-N.