I want to convey the idea of which I am selling books for people to think deeply, therefore, in short, I want to say 'books for thinking', but when I google it, there is no such phase, I am concerned that it doesn't make sense to native speakers. Actually, I found someone said 'book on thinking'.
A slogan or title like that isn't expected to be a complete, grammatically correct sentence. I know what you mean. I presume most people would know what you mean. So it's perfectly good and valid.
"Book on thinking" would be a very different thing. I'd understand that to mean a book about how the mind works. In once sense or another: I'd imagine it could be anything from a book about the physics and chemistry of the brain to a philosophical discussion about the nature of the mind.
Books for (Deep) Thinkers
It's not an especially elegant turn of phrase, but it is frequently used.
For some reason the noun for the person has come to sound better than the gerund for the activity. Likely, this is because thinking is itself not particularly special, since everyone regularly thinks. This undermines your intention to describe the process of thinking interesting or unusual thoughts.
In contrast, a thinker is by definition, someone who spends a lot of time thinking about deep or significant things, or someone with demonstrated intellectual prowess.
If you really want to focus on the process of thinking, then it might be better to use a more grandiose word, for example:
Books on Cogitation
I think "books on thinking" would refer to a book about thinking, while "books for thinking" would be closer to what you want. However, with "books for thinking," it's unclear if the reader ends up thinking more about the book itself, or if the book encourages the reader to think more about life itself.
I don't know how formal you want to get, but you might consider: Books to promote deeper thinking.