Summary: In this paper, a new test procedure is proposed to test a linear hypothesis of \(k\)-sample mean vectors in high-dimensional normal models with heteroskedasticity. The motivation is on the basis of the generalized likelihood ratio method and the Bennett transformation. The asymptotic distributions of the new test are derived under null and local alternative hypotheses under mild conditions. Simulation results show that the new test can control the nominal level reasonably and has greater power than competing tests in some cases. Moreover, numerical studies illustrate that our proposed test can also be applied to non-normal data.