Biometrics is the science and technology dealing with the measurement and analysis of the biological features of the human body. The analysis is based on comparing the value of certain measured features with the form features in the database. Unimodal Biometric Systems have many limitations regarding precision in the identification/authentication of personal data. To accurately identify a person, a multimodal biometrics system such as combining face and fingerprint characteristic is used. Many such multi-biometrics fusion possibilities exist that can be utilized as an authentication system. In this paper, we present a new authentication system of the multimodal biometrics method for both face and fingerprint characteristics based on general shape feature fusion vectors. There are two main phases in our method: first, the fused shape features for both face and fingerprint images are extracted in accordance with central moments, and second, these features were recognized for retrieval of an authorized person using direct Euclidian distance. Experimentally, we tested about 100 shape features vectors, and observed that our method allows to improve the multimodal biometrics model when we are using the same features for two biometric images. A new method has a high-performance precision when invariant moments are used to extract shape features vectors and when similarity measurements computed based on direct Euclidean distance in the experiments are performed. We recorded False Acceptance Rate, False Rejection Rate, and Accuracy, FAR and FRR where the accuracy of the model is 91 %.