Voldemort wanted to kill Harry because, above all else, he wanted to avert the prophecy. While it is true that he chose Harry Potter unbeknownst to him (it could have been Neville Longbottom), the protective spell of love he triggered when Lily tried to kill Harry was what protected Harry till he was old enough to become a wizarding student at Hogwarts.
When Harry began the quest to destroy Voldemort’s Horcruxes, Voldemort became more enraged and sought to kill him even more. Another reason why Voldemort may have wanted to kill Harry was that he, Harry, was in the way of him being the greatest wizard. Indeed, Voldemort’s bloodlust for Harry was tinged by a fear of Dumbledore and, quite honestly, Harry.
Despite his many attempts to avert the prophecy, one can agree that his efforts only worked to set things in stone to bring it to pass, and to fulfill Harry’s destiny.