Development of solid polymer electrolytes has potential applications for battery technology. Membranes should be environment friendly and also have high conductivity. We use chitosan, cellulose and graphene in this research. In this work, 1% (w/v) of chitosan powder and 1.5% (w/v) of acetic acid were dissolved in double distilled water. The solution was heated to 60°C under constant stirring until the chitosan powder was completely dissolved and a semi-transparent thick chitosan solution was obtained. To this chitosan solution, appropriate amounts of graphene (grade H5-XG Sciences) was added to have 5, 10, 20 and 30% graphene (weight with respect to chitosan). The solution was sonicated for dispersing graphene and then 100ml of it was poured on plastic dishes with and without cellulose fabric in it. The films were dried by slow evaporation technique. The sample thickness varied from 200 to 300µm. SEM images showed that chitosan film formed on cellulose and had grid like structures. Chitosan deposited more on the fibres of the cellulose. This is attributed to the rectangle shaped micro pores of cellulose fabric. From the cross section of the films, it was observed that graphene arranged in stacks along the plane of the cellulose fabric and the fabric became darker as graphene concentration increased. The dielectric properties such as dielectric constant, impedance, conductivity and dissipation factor were measured from 102 - 106 Hz. The conductivity of the sample increased as the frequency increased. The conductivity of the samples at room temperature increased with increase in graphene concentrations. The conductivity varied from 10-8 to 10-5 S/Cm as the graphene concentration increases from 0 to 30%. Hence conductivity increases significantly as graphene concentration increases. From the dissipation factor for the films, the relaxation process could be observed in the frequency ranging from 102 to 105 Hz. It is observed that as frequency increases, the relaxation tend to shift towards higher frequency indicating that graphene affects the relaxation of the polymer nanocomposite. At high frequency (106Hz) dissipation factor for cellulose fabric, chitosan in cellulose, chitosan with 5% graphene in cellulose, chitosan with 10% graphene in cellulose, chitosan with 20% graphene in cellulose, chitosan with 30% graphene in cellulose are 0.14, 0.19, 0.4, 0.8 and 1.38 respectively. This shows that dissipation factor increases as the graphene concentration increases. This implies that graphene improves heat dissipation in these films. The dielectric constant was observed to be maximum for chitosan with 30% graphene in cellulose indicating that the graphene may assemble into percolation networks at higher concentrations of graphene (20 and 30%).