Yes, but that sentence has a subtly different meaning than the one above. Your sentence here would mean "He wants to read a book", which is not the same as the original sentence "He wants a book to read". This sentence would be used when somebody is about to leave for the library, and one asks, "why is he leaving?" Answer: "he wants a book to read (and so he's going to the library to get one)".
Whereas your sentence is more appropriate when you see somebody walking away to sit down with a book already in her hand, and one asks "what does she want to do now?" Answer: "she wants to read a book (and so she's going to sit down to read the one in her hand)". You would not say "She wants a book to read", because she already has one in her hand.
I hope that was not too confusing, but I felt that we need to distinguish between these two sentences
Because I think that would be "Il veut lire un livre". These are two different sentences. The first sentence ( at least in English) would be used about somebody who is not in possession of a book, but they want to have one to read. The second one (your sentence) is more general, about somebody who just wants to read (a book). I'm sorry if this doesn't explain it properly...it is very subtle, but they are still two different meanings in English.
As a beginner I also find this confusing. This is a good site to begin to get the basics: http://french.about.com/library/prepositions/bl_prep_verbs.htm
Bonne chance !