This paper presents a parametric finite-difference scheme concerning the numerical solution of the one-dimensional Boussinesq-type set of equations, as they were introduced by Peregrine[16], in the case of waves relatively long with small amplitudes in water of constant depth. The method which is used can be considered as a generalization of the Crank-Nickolson method and it has been applied successfully to a problem used by Beji and Battjes.