I ask this because I couldn't find the answer elsewhere, and don't want to buy the Atlantean Edition without a confirmation first. Do I need any extra books such as D&D Player's or GM guide to play the Atlantean Edition of Conan RPG? Much appreciated.
You only need the Atlantean Edition Conan RPG in order to play the game. No other books are necessary.
You can access to the d20 SRD if you need to access the core d20 rules for some reason. But if you can -- it's never a bad idea to have the core D&D books (Player's Handbook, Dungeon Master's Guide, Monster Manual) around. But again, they're not necessary.
Likewise, the various Conan supplements, such as Hyboria's Fallen, Scrolls of Skelolos, and The Road of Kings, as other posters mentioned, are excellent additions to your game but -are not NECESSARY-.
Short Answer: You only need the Atlantean Edition Conan RPG core book. Enjoy.
To enjoy the RPG thoroughly I recommend buying many of Mongoose's Conan books. The only one I was not happy with was Free Companies. Obviously having a handy collection of REH's original Conan stories is the ABSOLUTE MUST, because the RPG is heavily based upon his stories, and to a lesser extent the comics of the past and present, or the movies. I recommend Road of Kings (a gazetteer, or atlas of sorts), Hyboria's Fiercest, Hyboria's Fallen, Hyboria's Finest. All the others are gravy. The hardback of the Core Rules is expensive, but (as a purchaser of the paperback edition only so far) I have heard that the Atlantean edition (the revised Core Rules) is packed with good stuff that is lacking in the paperback.