I'd like to know who is the first person that introduced the tree of phrase structure in linguistics.
"Tree" has been a thing in mathematics for some time. "Phrase structure" is a particular mathematical theory of syntax introduced by Chomsky. As far as I know the first phrase structure tree is on p. VI-205 (268) of "The logical structure of linguistic theory" (1955: original version), where he explains the "Q-derivation" (VI-203a) with a diagram, recognizable as the derivation of some strings (words could be used by he used "c1 c2 c3 c4" etc). The same analysis is given in his dissertation Transformational analysis, a reduction to essentials of part of LSLT. It depends on whether you mean "both tree, and PS analysis". Tree diagramming is older.
The French linguist Lucien Tesnière also used trees (called stemmas if I remember well). He has nothing to do with Chomsky, and is possibly older. I don't know if he inherited the idea of stemmas from somebody else. https://en.wikipedia.org/wiki/Lucien_Tesni%C3%A8re#Stemmas