There many articles in the web
if I translate an article to another language and put it in another website (with mentioning the source)
will it be illegal to do that?
Do I need author's permission before doing that?
This is illegal unless it is out of copyright under the laws of the U.S. and most other countries, unless you have the permission of the copyright owner.
A few countries allow a translation to be made into one of their national languages if one is not made within a certain number of years and a request to do so does not cause one to be made, without violating their country's copyright laws.