The author have collected and classified huge number of references for background. While I am writing the background section, if I use the references he used, but not the sentences and organization, is it still plagiarism?
It's not clear to me what you mean. If you just mean you learned a lot of references from the thesis and then cited those references when they seemed appropriate in your own writing, then there's nothing wrong with it. On the other hand, it's less appropriate if you are repeatedly imitating someone else's nontrivial choices about which papers to cite. I'm not sure where to draw the line between plagiarism and other inappropriate behavior, but you should avoid it in any case.
For example, suppose someone has carefully chosen ten representative references for each of six topics and made these citations when introducing these topics. If your background section includes different paragraphs describing the topics (so there's no copying of text) but offers exactly the same citations, then you're taking unfair advantage of that person's work by giving the impression that you chose and organized these references yourself. It's arguably not as bad as copying chunks of text, but it at least doesn't seem like good manners. (I'd be annoyed if I noticed that someone else's background section cited the exact same sixty papers as mine without giving me any credit.)
If this is the sort of thing you're talking about, then you should give credit by explaining the source. For example, you could write something like "For further background material, see [that thesis], from which I took many of the citations in this section."