I have an Australian friend who travels very often and I want to say to her
I really envy your traveling life
Is it right sentence? If not, what is nicer words?
The sentence is grammatically correct and sounds perfectly clear to me, but I think it would maybe sound a bit better if you said "lifestyle" instead of "life", as you're describing the way that they choose to live their life.
I envy your travelling lifestyle.
That sentence is correct. You can also say, "I really envy that you get to travel so much."
As a sentence your text is OK.
However "envy" can be seen as a negative thing, similar to jealousy.
I might alternatively say: "You are very lucky to travel so much"