Fractal geometries are found attractive to designers seeking for compact size mi- crowave circuits and antennas. In this paper, Peano fractal based open-loop resonators are adopted to design dual-band microstrip band-stop filters (PSFs). The suggested filter structure is essentially based on that of the conventional open-loop rectangular microstrip resonators. The resonators of the proposed PSF structure are made in the form of Peano fractal geometry with different iteration levels. Many filters have been modeled, and their performances have been eval- uated using a commercially available full-wave electromagnetic simulator. Each of the modeled filter structures contains two pairs of open loop fractal based resonators with different iteration levels. The lower frequency band-stop performance is attributed to the resonators with higher iteration level while the higher frequency band-stop performance is due to the resonators with lower iteration level. Simulation results for the proposed microstrip filters have confirmed the validity to realize compact dual-band narrow-stopband microstrip filters. A comparative study implies that higher size reduction of the realized filter has taken place as the iteration level of the fractal microstrip open-loop resonators becomes higher. The results presented show that the fractal-based resonators can be used to construct compact narrow-stopband filters suitable for a wide variety of the recently available communication applications.