We analyze radiation of a charge moving in a vacuum channel in an anisotropic non-gyrotropic medium with plasma-like components of the permittivity tensor. The expressions for field components are obtained and analyzed. It is shown that the field contains both the radiation field and the plasma oscillations. Most attention is focused on the energy loss of the charge per the unit path length. The dependencies of the loss on the charge velocity and the plasma frequencies are studied. The relative roles of radiation loss and polarization one are considered. The most interesting result is that the energy loss is negligible when one of the permittivity tensor components is equal to 1, and the charge velocity tends to the speed of light in vacuum. This effect can be promising for applying in collimators of ultrarelativistic bunches.