We numerically demonstrate an all-optical tunable dual-band double negative (DNG) index chirped metamaterial (MM) in the mid-infrared (M-IR) region. This MM possesses an ultrafast and significant tunability under low pump light power, realized by combining phase change material (PCM). It has a configuration of elliptical nanohole array (ENA) penetrating through metal/PCM/metal (Au-Ge(2)Sb(2)Te(5)-Au) films. Here, 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, which can achieve multiple internal surface-plasmon polariton (SPP) modes at the inner metal-dielectric interfaces of the structure and thus providing a dual-band negative index with simultaneous negative permittivity and permeability. The influence of amorphous and crystalline states of Ge(2)Sb(2)Te(5) on the effective optical parameters of the structure is analyzed. Switching between these states provides a large wavelength shift of the structure's effective optical parameters. A photothermal model is used to study the temporal variation of the temperature of the Ge(2)Sb(2)Te(5) layer to show a potential to switch the phase of Ge(2)Sb(2)Te(5) by optical heating. Generation of the tunable dual-band DNG index presents clear advantages as it possesses a fast tuning time of 0.4 ns, a low pump light intensity of 7.3μW/μm(2), and a large tunable wavelength range of 978 nm. We expect that our design may have potential applications in actively tunable multi-band nanodevices.