We propose to estimate the Hurst parameter involved in fractional processes via a method based on the Karhunen-Loève expansion of Gaussian process. We specifically investigate the cases of the fractional Brownian motion(fBm), the fractional Ornstein-Uhlenbeck(fOU) family and the fractional Brownian bridge(fBb). We numerically compare our results with the ones obtained by the maximum likelihood method, which show the validity of our proposal.