Abstract: Proximate series solutions of the output pulse waveforms and transmission efficiencies of transmission line with exponential impedance profile have been developed based on distributed-parameter model for typical incident pulses suitable for next generation of Z-pinch plasma drivers. The transmission efficiencies are studied computationally with these solutions for petawatt-class Z-pinch driver’s exponential transmission line taking account of the line’s length and ratio of output impedance to the input as well as the pulse’s shape and parameter. The voltage transmission efficiency increases with the increase of the ratio of output impedance to the input, line length and pulse frequencies; the power transmission efficiency increases with the increase of pulse frequencies and with the dec