  We consider the effects of Gravity's Rainbow on the self-sustained equation
which is responsible to find new traversable wormholes configurations powered
by their own gravitational quantum fluctuations. The form of the shape function
considered is obtained by imposing the equation of state $p_{r}=\omega \rho $.
We investigate the size of the wormhole as a function of the parameter $\omega$
in the phantom region. We discover that a wormhole which is traversable in
principle, but not in practice, can be produced.
