Military personnel have greater psychological stress and are at higher suicide attempt risk compared with the general population. High mental stress may cause suicide ideations which are crucially driving suicide attempts. However, traditional statistical methods could only find a moderate degree of correlation between psychological stress and suicide ideation in non-psychiatric individuals. This article utilizes machine learning techniques including logistic regression, decision tree, random forest, gradient boosting regression tree, support vector machine and multilayer perceptron to predict the presence of suicide ideation by six important psychological stress domains of the military males and females. The accuracies of all the six machine learning methods are over 98%. Among them, the multilayer perceptron and support vector machine provide the best predictions of suicide ideation approximately to 100%. As compared with the BSRS-5 score ≥7, a conventional criterion, for the presence of suicide ideation ≥1, the proposed algorithms can improve the performances of accuracy, sensitivity, specificity, precision, the AUC of ROC curve and the AUC of PR curve up to 5.7%, 35.9%, 4.6%, 65.2%, 4.3% and 53.2%, respectively; and for the presence of more severely intense suicide ideation ≥2, the improvements are 6.1%, 26.2%, 5.8%, 83.5%, 2.8% and 64.7%, respectively.