Wrinkles can be often observed in dielectric elastomer (DE) films when they are subjected to electrical voltage and mechanical forces. In the applications of DEs, wrinkle formation is often regarded as an indication of system failure. However, in some scenarios, wrinkling in DE does not necessarily result in material failure and can be even controllable. Although tremendous efforts have been made to analyze and calculate a variety of deformation modes in DE structures and devices, a model which is capable of analyzing wrinkling phenomena including the critical electromechanical conditions for the onset of wrinkles and wrinkle morphology in DE structures is currently unavailable. In this paper, we experimentally demonstrate controllable wrinkling in annular DE films with the central part being mechanically constrained. By changing the ratio between the inner radius and outer radius of the annular films, wrinkles with different wavelength can be induced in the films when externally applied voltage exceeds a critical value. To analyze wrinkling phenomena in DE films, we formulate a linear plate theory of DE films subjected to electromechanical loadings. Using the model, we successfully predict the wavelength of the voltage-induced wrinkles in annular DE films. The model developed in this paper can be used to design voltage-induced wrinkling in DE structures for different engineering applications.