Bipolar disorder is a serious psychiatric disorder characterized by periodic episodes of manic and depressive symptomatology. Due to the high percentage of people suffering from severe bipolar and depressive disorders, the modelling, characterisation, classification and diagnostic analysis of these mental disorders are of vital importance in medical research. Electroencephalogram (EEG) records offer important information to enhance clinical diagnosis and are widely used in hospitals. For this reason, EEG records and patient data from the Virgen de la Luz Hospital were used in this work. In this paper, an extreme gradient boosting (XGB) machine learning (ML) method involving an EEG signal is proposed. Four supervised ML algorithms including a k-nearest neighbours (KNN), decision tree (DT), Gaussian Naïve Bayes (GNB) and support vector machine (SVM) were compared with the proposed XGB method. The performance of these methods was tested implementing a standard 10-fold cross-validation process. The results indicate that the XGB has the best prediction accuracy (94%), high precision (> 0.94) and high recall (> 0.94). The KNN, SVM, and DT approaches also present moderate prediction accuracy (> 87), moderate recall (> 0.87) and moderate precision (> 0.87). The GNB algorithm shows relatively low classification performance. Based on these results for classification performance and prediction accuracy, the XGB is a solid candidate for a correct classification of patients with bipolar disorder. These findings suggest that XGB system trained with clinical data may serve as a new tool to assist in the diagnosis of patients with bipolar disorder.