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In this paper, a bandstop plasmonic filter with two wide bandgaps in Near-Infrared (NIR) and Mid-Infrared (MIR) wavelength bands is investigated numerically. The filter consists of double-sided square resonators end-coupled with a Metal-Insulator-Metal (MIM) waveguide via apertures. The wide bandgaps are achieved using a combination of square resonators which possess different relative permittivity and the same dimensional parameter. It is found that the stop wavelength ranges can be tuned by the number of square resonators with desired relative permittivity. Achieving the proper relative permittivity values may be difficult using general dielectrics; therefore, the resonators are filled by nanocomposite materials. The nanocomposite media are realized by poly-methyl-methacrylate (PMMA) and Ag nano-spheres. Also, there is a possibility of filter design at other ranges of NIR and MIR wavelength bands by changing the relative permittivity of the bus waveguide.