The preparation of 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BmImTFSI)-based poly(methyl methacrylate)–poly(vinyl chloride), PMMA–PVC, gel polymer electrolytes was done by solution casting technique. The ionic conductivity of gel polymer electrolytes was increased, up to a maximum value of (1.64 ± 0.01) × 10−4S/cm by adding 60 wt% of BmImTFSI. Conductivity–frequency dependence, dielectric relaxation, and dielectric moduli formalism were also further analyzed. These studies assert the ionic transportation mechanisms in the polymer matrix. Occurrence of polarization electrode–electrolyte interface is also observed. This leads to the formation of electrical double layer and hence indicates the non-Debye characteristic of the polymer matrix in the dielectric studies. Based on the changes in shift, changes in intensity, changes in shape, and existence of new peaks, attenuated total reflectance–Fourier transform infrared divulged the complexation between PMMA, PVC, lithium bis(trifluoromethanesulfonyl)imide, and BmImTFSI, as shown in the infrared spectra.