The incident light may induce surface plasmons noble-metal nanomaterials, which are the collective oscillations of the surface electrons in the metal. When the frequency of the surface plasmons matches the incident light, plasmonic resonance occurs with a special electro-magnetic and spectral property. Ultilizing this property, the spectral behavior of metallic nanomaterials can be adjusted. For example, by varying paramters including the size, shape, and dielectric constants the nanostructures’ background materials, the spectral signals can be effectively controled. So far, the surface plasmons of noble-metal nanomaterials with certain symmetries have been widely studied and applied. In addition, the spectral properties of asymmetric metallic nanostructures have also drawn great attention in the community. It has been shown that one important problem in designing plasmonic optical sensors in the visile-near infrared regime is how to achieve the effective control of key parameters of the extinction spectra, including the resonance wavelength, spectral width, and peak intensity. In this work, an asymmetric structure consisting of two silver nanorings is proposed. With the finite-difference time-domain method, the nanostructure’s extinction spectra are studied in the visible-near infrared regime by varying the parameters, including the rings’ radii, the separation, and the light’s polarization. The results indicate that two independent surface plasmons resonances are induced in the extinction spectra in the wavelength range of 0.4~3 μm. It is found from the electric fields that the resonances are correlated to two different electro-magnetic modes. It is also revealed that the two different resonance peaks in the extinction spectra can be independently adjusted by changing different parameters of the double nanorings. The shorter resonance wavelength and its spectral width can be tuned by varying the sizes of the nanorings, while the longer resonance wavelength and its spectral width can remain almost the same. Besides, The peak intensities of the two resonances can be adjusted in different trends by changing the nanorings’ separation or the polarization angle of the incident light. In this work, two plasmonic resonance peaks that can be respectively controled are revealed in the extinction spectra of the asymmetric silver double nanorings; the results shown in this work may provide us with theoretical foundations in the design of photoelectric sensors in the visible-near infrared region.