It's a singleplayer game. The "Online" is misleading; from what I understand, "Sword Art Online" is the name of the franchise that the game keeps referring to because they didn't have an idea for a story, so characters keep talking about things that happened on the Anime, other games, whatever.

Thanks for the reply first. I know SAO is the name. What I ask is if this game has story mode or other play mode for single player. Or this game only a co-op pve or gvg game?

Well, of course there's a story. It's just not very good, at least for me.

I don't really know what a "story mode" is supposed to be; I don't remember details like that, but if you play the game normally you'll be following the story. Whether there are any other modes, I don't remember (since I also don't care about multiplayer or similar stuff).

It's primarily a Singleplayer game with Multiplayer elements if you intend on grinding or simply socialising