The high-impedance property of an offset finite-ground microstrip line is utilized to construct an improved transmission-line electromagnetic bandgap (EBG) structure with enhanced bandgap width and attenuation. Using the self-calibrated method of moments (MoM), the two effective per-unit-length parameters are firstly extracted to demonstrate the fundamental frequency-dispersive characteristics of the guided wave in this EBG. Then, the transmission coefficients of the two finite-length EBG circuits with ideal impedance matching at two ports are characterized, thus exhibiting the distinctive bandstop and bandpass behaviors as the guided-wave propagates across this EBG with finite extended region. Finally, a five-cell EBG circuit, fed with the standard 50 feed lines, is further modeled to give an evident verification of its enhanced EBG performance.