Could you please suggest me several markets which are the nearest to Xian Jiaotong University?

Hi, do you mean the campus at the No. 28, Xianning West Road?
Yes, there is Vanguard Supermarket near the campus, 510 meters from the Northeast Gate. And it is located at the No.159 of Xinqing South Road.

BTW, the university is also very closer to Lifeng International where you can find stores, gyms, restaurants and cinema. It is also not very far from the Qinggong Market.