Adiabatic global potential energy surfaces, for singlet and triplet states of A' and A " symmetries, were computed for an extensive grid for a total of 8469 conformations of H-3(+) system at full configuration interaction ab initio level and using an extended basis set that has also been optimized for excited states. An accurate (root-mean-square error lower than 20 cm(-1)) global fit to the ground-state potential is obtained using a diatomics-in-molecules approach corrected by several symmetrized three-body terms with a total of 96 linear parameters and 3 nonlinear parameters. This produces an accurate global potential which represents all aspects of ground-state H-3(+) including the absolute minimum, the avoided crossing and dissociation limits, satisfying the correct symmetry properties of the system. The rovibrational eigenstates have been calculated up to total angular momentum J=20 using hyperspherical coordinates with symmetry adapted basis functions. The infrared spectra thus reproduced is within 1 cm(-1) with respect to the experimental values for several transitions.