The unique 4f orbitals and abundant electronic energy levels of rare earth elements enable effective doping and modification to enhance hydrogen storage performance, making it an increasingly prominent focus of research. The structures of neutral and cationic CeHn0/+ (n = 2-20) clusters have been determined using the Crystal Structure AnaLYsis by Particle Swarm Optimization (CALYPSO) method in conjunction with density functional theory (DFT). Interestingly, the CeH13 and CeH14+ exhibit remarkable stability in the doublet state with Cs and C2v symmetry, respectively. The adsorption energy of CeHn0/+ (n = 2-20) suggests a preference for H atoms to chemically adsorb on Ce atoms. The analysis of molecular orbital composition reveals that the stability of both CeH13 and CeH14+ is attributed to the significant hybridization between the H 1s and Ce 4f orbitals. Both CeH13 and CeH14+ demonstrate significant hydrogen storage capacities, with values reaching 8.5 wt% and 9.1 wt%, respectively.