The energy (due to matter plus fields including gravity) distribution of the Reissner-Nordstrom anti-de Sitter (RN AdS) black holes is studied by using the Moller energy-momentum definition in general relativity. This result is compared with the energy expression obtained by using the Einstein and Tolman complexes. The total energy depends on the black hole mass M and charge Q and the cosmological constant A. The energy distribution of the RN AdS is also calculated by using the M phi ller prescription in teleparallel gravity. We get the same result for both of these different gravitation theories. The energy obtained is also independent of the teleparallel dimensionless coupling constant, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model. In special cases of our model, we also discuss the energy distributions associated with the Schwarzschild AdS, RN and Schwarzschild black holes, respectively.