The ability of automatically modeling learners' personalities is an important step in building adaptive learning environments. Several studies showed that knowing the personality of each learner can make the learning interaction with the provided learning contents and activities within learning systems more effective. However, the traditional method of modeling personality is using self-reports, such as questionnaire, which is subjective and with several limitations. Therefore, this study presents a new unobtrusive method to model the learners' personalities in an intelligent Moodle (iMoodle) using Learning Analytic (LA) approach with Bayesian network. To evaluate the accuracy of the proposed approach, an experiment was conducted with one hundred thirty-nine learners in a public university. Results showed that recall, precision, F-measure and accuracy values are in acceptance range for three personality dimensions including extraversion, openness, and neuroticism. Moreover, the results showed that the LA approach has a fair agreement with the Big Five Inventory (BFI) in modeling these three personality dimensions. Finally, this study provides several recommendations which can help researchers and practitioners develop effective smart learning environments for both learning and modeling. For example, it is needed to help identify more features of the hardest personality traits, such as agreeableness, using gamification courses.