In this work we present, for the first time, calculations of resonance energies and widths for some high-lying doubly-excited resonance states of H- embedded in plasmas using the complex-coordinate rotation method. Screened Coulomb potentials of Debye-type are used to simulate the plasma effects. Correlation effects between all the charged particles are taken into consideration by using Hylleraas-type wave functions. Our predicted results are converged with the basis lengths up to N = 715. For the lowest lying 2s(21)S(e) state, good agreement has been found with an earlier calculation using the stabilization method. Results for the higher-lying 3s(21)S(e) and 4s(21)S(e) autoionization states of the plasma-embedded H- ion are the first calculations reported in the literature. (c) 2007 Elsevier B.V. All rights reserved.