Advanced studies on modern electronic devices using the filter function show the impact of multi-band filters on the electrical qualities of these devices. Due to the importance of its electromagnetic characteristics, the dual-band bandpass microwave filters can be used in several high-quality electronic devices. In this paper, a dual-band bandpass filter (DBBPF) is provided. The proposed filter is inspired by a pair of tapered split-ring metamaterial resonators of thesame asymmetric square coupled interlinked shape (SCI-SRR) and of different sizes. The choice of the two resonators, which have a negative permeability (${\mu}$${\le}$ 0), is made such that the magnetic resonance of each resonator appears inX-band. The designed filter consisting of these SCI-SRRs is fed in parallel mode by two microstrip lines and etched on the upper face of the used substrate. Both SCI-SRRs which are coupled to the feed lines are interconnected by a folded microstrip line to have the necessary miniaturization of the filter. The electrical dimensions of our DBBPF are (1.305 ${\lambda}_0$${\times}$0.913 ${\lambda}_0$) mm$^2$, for which ${\lambda}_0$ is the wavelength of the lowest frequency calculated at 9.89 GHz. Numerical calculations using the finite element method (FEM) based on high-frequency structure simulator software are performed to design this filter. The two filter bandwidths, which are obtained as a function of the rings widths of the tapered metamaterial resonators (${\alpha}$,${\beta}$), are considered in the X-band, they are of the order of 186.2 and 89.7 MHz, respectively. To validate our work, we compared our obtained results with the other recent work results for the same field of research.