Graphene has been intensively investigated as a possible hydrogen storage medium due to the spectacular properties granted by its two-dimensional nature. Since graphene's discovery, several new two-dimensional carbon allotropes have been theorized and synthesized. We investigated the hydrogen storage ability of six such allotropes: C-65, C-64, C-63 > C-62, C-31 and C-41. The ability to anchor lithium metal atoms over each allotrope and the hydrogen binding energies for each lithium decorated allotrope were studied with density functional theory using LDA, GGA and vdW-DF2 (for describing van der Waals interactions) functionals. All the allotropes were able to achieve double sided lithium decoration and hydrogen adsorption. Every allotrope other than C-31 possesed lithium binding energies stronger than bulk lithium's cohesive energy which indicates that adsorbed lithium atoms will not cluster on the allotrope surface. Furthermore, every structure produced hydrogen binding energies stronger than that of lithium decorated graphene, suggesting the potential of use of these structures in practical hydrogen storage media. The C-41 structure was able to adsorb far more hydrogen molecules than any other structure with a maximum hydrogen gravimetric density of 7.12 wt.% using the vdW-DF2 functional. Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.