Split ring resonators (SRRs)-based broadband metamaterial filters have attracted considerable attention due to their great prospect of practical applications. These filters had been usually obtained by stacking multiple different-sized metallic patterns, making their fabrication quite troublesome. Herein, we presented a simple design of broadband filter composed of two nested SRRs. The resonance bandwidth of the metamaterial filter gradually increased with the decrease of the arm length of the inner SRR. The increase in the resonance bandwidth was attributed to the increase in the radiation of the entire structure. Moreover, the bandwidth of the metamaterial can be further broadened by decreasing the period of the structure. The proposed filter provides a meaningful way toward expanding the bandwidth operating range from narrowband to broadband in an effective way.