In this paper, a new capacitively stepped-impedance resonator (CSIR) is proposed to develop the microstrip squareloop dual-mode bandpass filter. Using this new design, simultaneous size reduction and spurious response suppression for the dual-mode bandpass filter can be achieved. An analytical formulation of this novel resonator is given in order to elucidate the spurious frequencies relocation design. Together with this formulation, a generalized dual-mode bandpass filter model is developed so as to ease the analysis of transmission zero and insertion loss. A prototype filter is designed at 900 MHz with 1.5% fractional bandwidth. Significant spurious suppressions up to 33 and 35 dB are measured at 1.8 and at 2.7 GHz, respectively. A circuitry size reduction of 54% is achieved when compared with that of the conventional structure. Moreover, the CSIR allows frequency tuning and, thus, a varactor-tuned filter is designed and a measured tunable center frequency between 1.5-1.62 GHz is demonstrated. Utilizing the proposed structure, not only size reduction, as well as spurious response suppression, but also center frequency tuning can be achieved.