This study is aimed to elaborate the energy problem of general wormhole space-times in two different approaches of gravity such as general relativity and teleparallel gravity. In this connection, the energy for well-known wormhole space-times is evaluated using Møller energy-momentum prescription in these different approximations. We obtained that energy distributions of Møller definition give the same results for various wormhole space-times in general relativity (GR) and teleparallel gravity (TG). The results strengthen the importance of Møller energy-momentum definitions in given space-times and viewpoint of Lessner that Møller energy-momentum complex is a powerful concept for energy and momentum.