The motion of the paraelectric-ferroelectric interface in KNbO3 at a hydrostatic pressure is studied in the framework of the mean-field theory. The kink solution is applied to the calculations of the width and velocity of the interface at different pressures. The calculations are based on the experimental data for the Curie-Weiss constant and the parameter of the Ginzburg-Landau expression for the free energy. The response of the interface motion to the hydrostatic pressure and the tricritical point is investigated nonempirically.