We analyze the energetics of three rotational gating mechanisms of an ion channel in the presence of a negative hydrophobic mismatch. To evaluate the free energy of the membrane deformation during the gating process, we use the continuum model imposing a strong hydrophobic interaction at the interface of the channel proteins and the nearby lipid molecules. Three gating mechanisms describe three different transitions from a conical closed state to one bottle-neck and two cylindrical open states. Differently from the situation of a positive hydrophobic mismatch, all three open states can be energetically favorable without introducing a spontaneous curvature although a quite strong surface tension of the membrane is required if the thickness change of the membrane does not cost any energy. We also discuss the effect of the thickness change of the membrane on the gating energy.