Dynamic facial expression recognition has many useful applications in social networks, multimedia content analysis, security systems and others. This challenging process must be done under recurrent problems of image illumination and low resolution which changes at partial occlusions. This paper aims to produce a new facial expression recognition method based on the changes in the facial muscles. The geometric features are used to specify the facial regions i.e., mouth, eyes, and nose. The generic Fourier shape descriptor in conjunction with elliptic Fourier shape descriptor is used as an attribute to represent different emotions under frequency spectrum features. Afterwards a multi-class support vector machine is applied for classification of seven human expression. The statistical analysis showed our approach obtained overall competent recognition using 5-fold cross validation with high accuracy on well-known facial expression dataset.