In this paper, we propose a method for user Finger Vein Authentication (FVA) as a biometric system. Using the discriminative features for classifying theses finger veins is one of the main tips that make difference in related works, Thus we propose to learn a set of representative features, based on autoencoders. We model the user finger vein using a Gaussian distribution. Experimental results show that our algorithm perform like a state-of-the-art on SDUMLA-HMT benchmark.