This paper presents a parametric finite-difference scheme concerning the numerical solution of the onedimensional Boussinesq-type set of equations, as they were introduced by Beji and Nadaoka [2] in the case of waves relatively long with small amplitudes in water of varying depth. The proposed method, which can be considered as a generalization of the Crank- Nickolson method, aims to investigate alternative approaches in order to improve the accuracy of analogous methods known from the bibliography. The resulting linear finite-difference scheme has been applied successfully to the bathymetry used by Beji and Battjes [1] as well as in an analogous one known in the bibliography as the Ohyama’s experiment [5] giving numerical results which are in agreement with the corresponding results given by MIKE 21 BW [4] developed by DHI Software.