Color face recognition has more attention recently since it considered one of the most popular biometric pattern recognitions. With a considerable development in multimedia technologies, finding a suitable color information extraction from color images becomes a hard problem. Several color face recognition methods have been developed. However, these methods still suffer from some limitations, such as increasing the number of extracted features, which leads to an increase in computational time. Besides, among those features some of them are redundant and irrelevant that will influence the quality of the recognition. Therefore, this paper presents a novel color face recognition method that depends on a new family of fractional-order orthogonal functions, which is called orthogonal fractional-order exponent functions. Then, using these functions as the basis functions of novel multi-channel orthogonal fractional-order exponent moments (FrMEMs), these novel descriptors are defined in polar coordinates over the unit circle and have many characteristics. A set of experimental series are performed using a set of well-known color face recognition and compared with other CFR techniques. Besides, a group of feature selection methods with different classifiers used to evaluate the number of extracted features is suitable or needs to be enhanced. Experimental results illustrate that the proposed method based on FrMEMs outperforms other CFR methods. As well as, the recognition rate doesn’t influence by reducing the number of features using different FS methods.