This paper presents a varactor- and stub-loaded dumbbell-shaped resonator (VSDSR) for application in differential dual-band bandpass filter, which possesses a tunable lower passband and a fixed upper passband. Under differential-mode (DM) bisection, the VSDSR behaves as a ring resonator with four resonant modes, which can be categorized into two independent groups for constructing two passbands. At the same time, the common-mode (CM) equivalent circuit of the VSDSR generates multiple CM resonant frequencies and some of them inevitably overlap with the DM ones. Accordingly, the traditional CM suppression methods such as adding shunt stub or lumped element are disabled. To suppress the CM signals in both DM passbands, the defected ground structure (DGS) units are embedded underneath the adjacent edges of the two rings directly to form a CM suppression filter without increasing the circuit size. Meanwhile, they have almost no effect on the DM responses. Benefitting from the bandstop and slow-wave effects of the employed DGS units, the CM noises in both DM bands can be rejected effectively. In particular, the level of the CM suppression in the DM lower passband can be improved by adjusting the location of the DGS units. Furthermore, the proposed CM suppression scheme is adaptive in the tunable lower DM passband.