Due to the harshness of underwater environment, size estimation of underwater network is difficult using conventional protocol techniques. A statistical signal processing approach of size estimation is proposed for this purpose using cross-correlation of Gaussian signals, which is effective for any environment networks. Limited bandwidth of underwater communications channel poses constraint on using Gaussian signal, which has infinite bandwidth. The aim of this paper is to investigate the effect of this limited bandwidth in crosscorrelation based underwater network size estimation using Gaussian signals with finite bandwidth.Index Terms-Cross-correlation function (CCF); effect of bandwidth; size estimation; underwater acoustic channels; underwater wireless communication network (UWCN).