Results are presented for highly accurate ab initio variational calculation of the rotation-vibration energy levels of H2O2 in its electronic ground state. These results use a recently computed potential energy surface and the variational nuclear-motion programs WARV4, which uses an exact kinetic energy operator, and TROVE, which uses a numerical expansion for the kinetic energy. The TROVE calculations are performed for levels with high values of rotational excitation, J up to 35. The purely ab initio calculations of the rovibrational energy levels reproduce the observed levels with a standard deviation of about 1 cm(-1), similar to that of the J = 0 calculation, because the discrepancy between theory and experiment for rotational energies within a given vibrational state is substantially determined by the error in the vibrational band origin. Minor adjustments are made to the ab initio equilibrium geometry and to the height of the torsional barrier. Using these and correcting the band origins using the error in J = 0 states lowers the standard deviation of the observed-calculated energies to only 0.002 cm(-1) for levels up to J = 10 and 0.02 cm(-1) for all experimentally known energy levels, which extend up to J = 35.