A well designed band stop filter is a compulsion of today's communication systems in order to suppress spurious bands for error free transmission and reception. While, with the advancement in modern wireless technologies, dual band equipped systems are getting more prominent for enhancing the system performance. A compact dual-band band stop filters are desired for better suppression and high selectivity of these systems, and hence enhances user experience. In this paper, a compact Dual-Band Band Stop Filter (DBBSF) has been presented. The studied structure incorporates the two S-shaped parallel connected quarter wavelength stubs. These two stubs are acting as a source for actualizing the two stop bands and the fractal line technique has been utilized for optimizing the filter size. The filter characteristics has been analysed theoretically and validation has been performed by using full wave electromagnetic simulation. In recent times, designing a dual band filter with high performance, compact size, and low cost are prerequisite for enriching the system performance. Therefore, in this paper, size reduction phenomenon by using fractal structure is implemented. The filter occupies small area of 16.2 mm * 16 mm on a substrate material with dielectric permittivity of 2.55. The proposed design of the Dual-band bandstop filter achieved attenuation of 37 and 49 dB at 1.9 and 5.5 GHz, respectively.