Personal identification technology as security systems is developing rapidly. Traditional authentication modes like key; password; card are not safe enough because they could be stolen or easily forgotten. Biometric as developed technology has been applied to a wide range of systems. According to different researchers, vein biometric is a good candidate among other biometric traits such as fingerprint, hand geometry, voice, DNA and etc for authentication systems. Vein authentication systems can be designed by different methodologies. All the methodologies consist of matching stage which is too important for final verification of the system. Neural Network is an effective methodology for matching and recognizing individuals in authentication systems. Therefore, this paper explains and implements the Neural Network methodology for finger vein authentication system. Neural Network is trained in Matlab to match the vein features of authentication system. The Network simulation shows the quality of matching as 95% which is a good performance for authentication system matching.