An Intelligent Biometrics systems aims at localizing and detecting human faces from supplied images so that further recognition of persons and their facial expression recognition will be easy. The area of human-computer interaction (HCI) will be much more effective if a computer is able to recognize the emotional state of human being. Emotional states have a greater effect on the face which can tell about mood of a person. So if we can recognize facial expressions, we will know something about the human's emotions and mood. This paper focuses on the novel Hybrid Facial Geometry Algorithm (HFGA) and comparative analysis of Facial Geometry algorithm and HFGA for facial feature extraction and its use to classify facial expressions. Feed forward back propagation neural network (BPNN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) are used as classifiers for expression classification and recognition. Experimentations are carried out using Japanese Female Facial Expression (JAFFE) database. Experimental results shows that average recognition efficiency from 95.33% to 93.33% is achieved for 30 to 75 test samples using BPNN and 95.71% to 95.33% with ANFIS approach.