The sorption of hydrogen isotopes by a composite nanostructured carbon material containing palladium clusters with an average size of 3–5 nm was studied in the temperature range of 8–290 K. The total amount of sorbed hydrogen strongly depends on the method of manufacturing the composite and is 2–4.5% of the sample mass. In the kinetics of hydrogen sorption and desorption by a composite, two processes with characteristic times differing by more than an order of magnitude are identified. The relatively fast process seems to be related to the filling of the cavities of the carbon matrix with hydrogen molecules, the longer one corresponded to the diffusion of hydrogen into the crystal lattice of palladium nanoclusters. Two temperature regions are found for the temperature dependences of the diffusion coefficients of hydrogen and deuterium in composite samples. Above 60 K, the diffusion activation energies in the sample containing palladium nanoclusters were more than twice the values obtained for the pure carbon matrix. Below 60 K, the diffusion coefficients of deuterium in the pure carbon matrix weakly depended on temperature. In the case of diffusion of hydrogen and deuterium into palladium nanoclusters, a change in the character of the temperature dependence was observed at a lower temperature (∼30 K). Below this temperature the activation energy decreased by approximately an order of magnitude.