<p>A novel univariate Legendre polynomial method is proposed for probabilistic failure load prediction in composite open-hole laminate based on the dimension-reduction method and Legendre polynomial. The effectiveness of the method was verified by comparison with experimental results. The mean prediction error was less than 3%, and the coefficient of variation of the prediction error was less than 15%, indicating that the new method can effectively predict the probabilistic failure load of composite open-hole laminate. In addition, ULAM was compared with RSM and Kriging model to verify its superiority. Given the same number of sample points, ULAM achieved higher prediction accuracy than the other two models. Finally, the effect of the polynomial order on the prediction accuracy of ULAM was investigated. If the order is too low, underfitting will occur. While increasing the order can improve the prediction accuracy, an excessively high order leads to overfitting, which in turn degrades the model’s performance.</p>