Vibrational levels of HOOH up to 6000 cm(-1) are accurately determined on a newly developed ab initio potential using the Lanczos algorithm. The six-dimensional Hamiltonian is discretized in terms of a direct-product potential optimized discrete variable representation (DVR) for the radial coordinates and a non-direct product finite basis representation (FBR) comprised of uncoupled spherical harmonics for the angular coordinates. The action of the potential energy operator is calculated on a direct-product grid via a factorized FBR-DVR transformation. All energy levels below 3000 cm(-1) are assigned and compared with existing theoretical and experimental data.