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Analytical model of convection in a thick horizontal cloud layer with free upper and lower boundaries is constructed. The cloud layer is supposed to be subjected to the Coriolis force due to the cloud rotation, which is a typical condition for tornado formation. It is obtained that convection in such system can look as just one rotating cell in contrast to the usual many-cells Benard convection.The tornado-type vortex is different from spatially periodic convective cells because their amplitudes vanish with distance from the vortex axis. The lower boundary at this convection can substantially move out of the initially horizontal cloud layer forming a single vertical vortex with intence upward and downward flows. The results are also applicable to convection in water layer with negative temperature gradient.