Many secondary prediction methods have been studied, but the prediction accuracy is still unsatisfactory, since beta-sheet prediction is difficult. In this research, we gathered statistics of pairs of three residue sub-sequences in beta-sheets, calculated propensities for them. When a sequence is given, all possible three residue sub-sequences are examined whether they form beta-sheets. A short coming is that many false predictions are made. To exclude false predictions and improve the prediction, we employed a Hopfield neural network, in which the natural limitations on protein tertiary structure and preference of chemically stable long beta-sheet are expressed in a form of energy functions. To clarify the prediction for heads and tails of beta-sheets, special variables are introduced, which are similar to the line process proposed by Geman.