A double-Lorentz (DL) transmission line (TL) metamaterial is proposed for the first time. Both effective material parameters µeff and "eff of the corresponding line exhibit a Lorentz-type dispersion, hence the proposed terminology double-Lorentz. This type of TL presents the interest of being intrinsically tri-band, while the previously reported composite right/left-handed TL metamaterial is only dualband. The DL TL theory is fully derived and demonstrated experimentally by a microstrip implementation. The tri-band property of the DL TL is illustrated by the design of a triband lamda/4 impedance transformer and a systematic design procedure is described.