Recently, facial expression recognition has attracted much attention in machine vision research because of its various applications. Accordingly, many facial expression recognition systems have been proposed. However, the majority of existing systems suffer from a critical problem: geometric variability. It directly affects the performance of geometric feature-based facial expression recognition approaches. Furthermore, it is a crucial challenge in appearance feature-based techniques. This variability appears in both neutral faces and facial expressions. Appropriate face geometry normalization can improve the accuracy of each facial expression recognition system. Therefore, this paper proposes different geometric models or shapes for normalization. Face geometry normalization removes geometric variability of facial images and consequently, appearance feature extraction methods can be accurately utilized to represent facial images. Thus, some expression-based geometric models are proposed for facial image normalization. Next, local binary patterns and local phase quantization are used for appearance feature extraction. A combination of an effective geometric normalization with accurate appearance representations results in more than a 4% accuracy improvement compared to several state-of-the-arts in facial expression recognition. Moreover, utilizing the model of facial expressions which have larger mouth and eye region sizes gives higher accuracy due to the importance of these regions in facial expression.