A phase behavior around the transition between ice VII and a plastic phase of water is investigated by molecular dynamics simulation and the subsequent analysis on the basis of Landau theory. The prior works have predicted that the phase transition between ice VII and plastic ice is a first-order transition on the ground of a weak hysteresis and so on. A rigorous survey in the present report, however, augments their prediction with new evidence that a first-order phase transition line gives way to a second-order one at higher pressures, where a tricritical point joins these phase boundaries together. Critical phenomena are also observed whereby, other than that associated with the hypothetical critical point in the deeply supercooled state, which could influence the physical properties in a wide range of temperatures and pressures. A new critical behavior is affirmed by the result that the scaling law holds at any pressure on the second-order phase transition line for which the critical exponents are estimated. We introduce an appropriate order parameter to obtain the Landau free energy functional and the change in the functional against temperature accounts for the phase behaviors. This also enables an estimate of the coexistence and the spinodal lines at pressures below the tricritical point, all of which compensate those obtained directly by molecular dynamics simulations. These results allow us to anticipate that the critical fluctuations may give us a clue for determining the phase boundary experimentally.