To implement a wideband bandpass filter with improved skirt-selectivity and out-band characteristics, a new parallel-coupled three-line unit with two short-circuited stubs symmetrically-loaded at the center line is proposed. Unlike most traditional ones, the passband of the proposed parallel-coupled three-line structure is based on the cross-coupling between non-adjacent lines rather than the direct-coupling between adjacent ones, whereas a pair of attenuation poles is found in the stopbands. After revealing its work mechanism, an efficient filter-design-scheme is correspondingly proposed for the presented structure. Firstly, based on a chebyshev-filter synthesis theory, a wideband passband filter consisting of a parallel-coupled two-line and two short-circuited stubs loaded at the input- and output- ports is designed. Furthermore, by putting a properly-designed 3/4-wavelength stepped-impedance resonator (SIR) in between the parallel-coupled two lines, two attenuation poles are then realized at the frequencies very close to the cutoff ones. Accordingly, the roll-off characteristics of the filter are significantly-improved to greater than 100,dB/GHz. Furthermore, two-section open-ended stubs are used to replace the short-circuited ones to realize a pair of extra attenuation poles in stopbands. To validate the proposed techniques, a wideband filter with a bandwidth of 3--5,GHz (Fractional bandwidth (FBW) $= (5,GHz-3,GHz)/4,GHz =50%)$ was designed, simulated, fabricated and measured. The measured responses of the filter agree well with the simulation and theoretical ones, which validates the effectiveness of the newly-proposed three-line unit and the corresponding design scheme.