Can someone become an UI designer when he does not major in UI?

Definitely yes. Nothing in the world is difficult for one who sets his mind into it. With proper methods and persistent efforts, one can make it without any basis.

To learn UI design from zero-basis, what kinds of knowledge should we know? Where do we begin our study? How to study systematically?

First of all, what kinds of skills should UI designers develop?

In terms of visual design, an UI designer should master the competence of: plane constitute; color composition; format design; psychology; art painting; design consciousness.

In terms of interactive design, an UI designer should master the competence of: acquaintance of user experience design principles; information mining, user research and data analysis; excellent logic; psychology; product visual sensation; communication.