In this article, a sixth-order differential narrowband high-temperature superconducting (HTS) common-mode filter (CMF) is presented. First of all, based on the proposed superconducting composite right-/left-handed (SCRLH) resonator, the equivalent lumped-element circuit models of differential-mode (DM) and common-mode (CM) are established, with the resonant frequencies derived and element values extracted. Then, the dispersion diagram and unloaded quality factor (Q_u) are plotted to demonstrate the intrinsic properties of wide stopband and low losses. Meanwhile, the relationship between structural parameters and DM rejection bandwidth is also explored. Finally, to verify the mentioned merits of SCRLH unit, a differential narrowband CMF circuit is taken into implementation with the constructed electromagnetic coupling types studied for better CM noise suppression and multiple transmission paths to generate out-of-band transmission zeros. Experimental results of the fabricated prototype with HTS technology are in good accordance with the simulations so as to demonstrate the increased DM rejection band, high CM suppression, and low insertion losses. Thus, the design theory has been validated as good potential to apply to superconducting receiver of high sensitivity and anti-CM noise interference.