A one-dimensional acoustic negative refractive index metamaterial based on the transmission line approach is presented. This structure implements the dual transmission line concept extensively investigated in microwave engineering. It consists of an acoustic waveguide periodically loaded with membranes realizing the function of series ?capacitances? and transversally connected open channels realizing shunt ?inductances.? Transmission line based metamaterials can exhibit a negative refractive index without relying on resonance phenomena, which results in a bandwidth of operation much broader than that observed in resonant devices. In the present case, the negative refractive index band extends over almost one octave, from 0.6 to 1 kHz. The developed structure also exhibits a seamless transition between the negative and positive refractive index bands with a zero index at the transition frequency of 1 kHz. At this frequency, the unit cell is only one tenth of the wavelength. Simple acoustic circuit models are introduced, which allow efficient designs both in terms of dispersion and impedance, while accurately describing all the physical phenomena. Using this approach, a good matching at the structure terminations is achieved. Full-wave simulations, made for a 10-cell-long structure, confirm the good performances in terms of dispersion diagram, Bloch impedance, and reflection and transmission coefficients.