Climacograptus was named by Hall (1865) [Sepkoski's age data: O Aren-u O Ashg-u Sepkoski's reference number: 1066]. It is the type genus of Climacograptacea. It was considered unknown by Storch et al. (2011).

It was reranked as Graptolithus (Climacograptus) by White (1874); it was reranked as Diplograpsus (Climacograptus) by McCoy (1874).

It was assigned to Diplograpsus by McCoy (1874); to Graptolithus by White (1874); to Graptoloidea by Sepkoski (2002); to Climacograptacea by Mitchell et al. (2007); to Diplograptidae by Kiessling (2008); to Climacograptoidea by Storch et al. (2011); and to Climacograptidae by Chen et al. (2016).