We present numerical modelling of a dual-band double-negative chirped metamaterial (MM) in the optical region. The MM has an elliptical nanohole array (ENA) penetrating through a metal/dielectric material/metal (Au-Al2O3-Au) film. We consider the case when the chirp is introduced by displacing the positions of the ENA along the short axis of the elliptical apertures inside the primitive cell. We demonstrate that these chirped MMs can provide a dual-band negative refractive index (NRI) with simultaneous negative permittivity and permeability in both near infrared (N-IR) region and mid-infrared (M-IR) region, respectively. As the neighboring elliptical holes are moved closer to each other the NRI in the N-IR region blue shifts to the shorter wavelength with a decreasing magnetic resonance, whereas the NRI in the M-IR region red shifts to the longer wavelength with an increasing magnetic resonance. This structure possesses a high value of figure-of-merit owing to the large size of the elliptical apertures.