Numerical computation based on a zero-dimensional thin-plasma-shell model has been carried out to study the scaling of the maximum kinetic energy per unit length, the current amplitude and the compression ratio for the imploding Z-pinch liner driven by peaked current pulses. A dimensionless scaling constant of 0.9 with an error less than 10% is extracted at the optimal choice of the current and liner parameters. Deviation of the chosen experimental parameter from the optimal exerts a minor influence on the kinetic energy for wider-shaped and slower-decaying pulses, but the influence becomes significant for narrower-shaped and faster-decaying pulses. The computation is in reasonable agreement with experimental data from the Z, Satu, Blackjack 5 and Qiangguang-I liners.