Facial expressions can tell a lot about an individual’s emotional state. Recent technological advances opening avenues for automatic Facial Expression Recognition (FER) based on machine learning techniques. Many works have been done on FER for the classification of facial expressions. However, the applicability to more naturalistic facial expressions remains unclear. This paper intends to develop a machine learning approach based on the Delaunay triangulation to extract the relevant facial features allowing classifying facial expressions. Initially, from the given facial image, a set of discriminative landmarks are extracted. Along with this, a minimal landmark connected graph is also extracted. Thereby, from the connected graph, the expression is represented by a one-dimensional feature vector. Finally, the obtained vector is subject for classification by six well-known classifiers (KNN, NB, DT, QDA, RF and SVM). The experiments are conducted on four standard databases (CK+, KDEF, JAFFE and MUG) to evaluate the performance of the proposed approach and find out which classifier is better suited to our system. The QDA approach based on the Delaunay triangulation has a high accuracy of 96.94% since it only supports non-zero pixels, which increases the recognition rate.