Hydrogen adsorption on pristine graphene (PG), graphene with defect (GD), and transition metal (TM) (Ag, Au, Cu, and Fe) doped graphene is systematically investigated for potential hydrogen storage using density functional theory. The stability of the TM atom doped graphene has been analysed by studying the binding energy and the electron density distribution. The TM atom-doped GD shows better binding energy and electron density overlap than PG; therefore, the TM/GD system has been considered and analysed for hydrogen adsorption. The hydrogen adsorption property is studied by examining the adsorption energy, mode of H₂, density of states (DOS), charge density difference, and Löwdin charges before and after adsorption to find a better TM/GD system for hydrogen storage. The Fe/GD system shows higher hydrogen adsorption energy and hydrogen in its stable Kubas mode. Furthermore, two to five H₂ molecule adsorption and desorption is studied. The increase in the number of H₂, which changes the DOS at the Fermi level, suggests that one can predict H₂ concentration by measuring conductivity changes. The present work is focused on studying the interaction between H₂ and TM/GD systems, which will help understand the basic adsorption mechanism for practical hydrogen storage.