We propose that dual-band coherent perfect absorption in the infrared can be achieved in a metasurface, which contains periodical symmetrically patterned elliptical graphene array on both sides of the silicon dioxide film. The physical mechanism of dual-band absorption is that the major and minor axes of the elliptical graphene disk have different widths and can produce resonances at different frequencies. Based on the independent resonances, the asymmetrically patterned metasurface can separately absorb light of different frequencies for TE and TM polarizations, which is useful to detect the polarization of incident light. In addition, the coherent absorptivity of each peak can be tuned by phase modulation and the dual-band absorption frequencies can be flexibly adjusted by changing the Fermi level of the graphene via chemical or electronic doping. Therefore, our proposed metasurface can achieve the double modulation for both absorption frequency and absorptivity, which make it a good candidate for optical switch and absorption modulator.