The channels used to convey the human emotions consider actions, behaviours, poses, facial expressions, and speech. An immense research has been carried out to analyse the relationship between the facial emotions and these channels. The goal of this study is to develop a system for Facial Emotion Recognition (FER) that can analyse the elemental facial expressions of human, such as normal, smile, sad, surprise, anger, fear, and disgust. The recognition process of the proposed FER system is categorised into four processes, namely pre-processing, feature extraction, feature selection, and classification. After preprocessing, scale invariant feature transform -based feature extraction method is used to extract the features from the facial point. Further, a meta-heuristic algorithm called Grey Wolf optimisation (GWO) is used to select the optimal features. Subsequently, GWO-based neural network (NN) is used to classify the emotions from the selected features. Moreover, an effective performance analysis of the proposed as well as the conventional methods such as convolutional neural network, NN-Levenberg–Marquardt, NN-Gradient Descent, NN-Evolutionary Algorithm, NN-firefly, and NN-Particle Swarm Optimisation is provided by evaluating few performance measures and thereby, the effectiveness of the proposed strategy over the conventional methods is validated.