The Richtmyer–Meshkov instability on a three-dimensional single-mode light/heavy interface is experimentally studied in a converging shock tube. The converging shock tube has a slender test section so that the non-uniform feature of the shocked flow is amply exhibited in a long testing time. A deceleration phenomenon is evident in the unperturbed interface subjected to a converging shock. The single-mode interface presents three-dimensional characteristics because of its minimum surface feature, which leads to the stratified evolution of the shocked interface. For the symmetry interface, it is quantitatively found that the perturbation amplitude experiences a rapid growth to a maximum value after shock compression and finally drops quickly before the reshock. This quick reduction of the interface amplitude is ascribed to a significant Rayleigh–Taylor stabilization effect caused by the deceleration of the light/heavy interface. The long-term effect of the Rayleigh–Taylor stabilization even leads to a phase inversion on the interface before the reshock when the initial interface has sufficiently small perturbations. It is also found that the amplitude growth is strongly suppressed by the three-dimensional effect, which facilitates the occurrence of the phase inversion.