Artin groups, also called Artin-Tits groups, have been widely studied since their introduction by Tits in 1960s. In particular, Artin groups are important examples in geometric group theory. For various non-positively curved or negatively curved properties on discrete groups, Artin groups are interesting targets. In this talk, we treat acylindrical hyperbolicity of Artin groups. Charney and Morris-Wright showed acylindrical hyperbolicity of Artin groups of infinite type associated with graphs that are not joins, by studying clique-cube complexes and the actions on them. By developing their study and formulating some additional discussion, we demonstrate that acylindrical hyperbolicity holds for more general Artin groups. Indeed, we are able to treat Artin groups of infinite type associated with graphs that are not cones. This talk is based on a joint-work with Shin-ichi Oguni (Ehime University).