The perfect optical vortex (POV), the ring size being independent of its topological charge, has found potential applications in optical tweezers and optical communications. In this Letter, we report a new kind of POV, termed as double-ring POV (DR-POV), whose diameters of the two rings are independent of topological charge. We theoretically demonstrate that such a vortex is the Fourier transform of an azimuthally polarized Bessel beam. Experimental results agree well with theoretical prediction. We further investigate the vortex nature of the DR-POV through an interferometric method, showing that the two rings of the vortex have the same topological charge value (magnitude and sign). The specular properties of the DR-POV may find application in optical tweezers, such as trapping and rotating of low-refractive-index particles in the dark region between the two rings. (C) 2019 Optical Society of America