We report converged full-dimensional quantum dynamical calculations of the vibrational relaxation in the collision: H-2 (v(1) = 1, j(1) = 0,1) + H-2 (v(2) = 0, j(2) = 0,1) --> H-2 (v'(1) = 0, j'(1)) + H-2 (v'(2) = 0, j'(2)), employing a recent global potential energy surface fitted to a large number of high-level ab initio points. The scattering dynamics is characterized by a time-independent wave packet approach based on the Chebyshev polynomial expansion of Green's operator, which requires repetitive calculations of the action of the system Hamiltonian onto the propagating wave packet. The full-dimensional Hamiltonian within the coupled-states approximation is discretized in a mixed grid/basis representation with the adaptation of the parity and diatomic exchange symmetry, and its action is efficiently computed in the appropriate representation facilitated by a series of one-dimensional pseudospectral transformations. Scattering involving both p- and o-H-2 are studied. Rate constants up to a high temperature (3500 K) are obtained from S-matrix elements and compared with available experimental measurements as well as with previous theoretical results.