Speaker recognition system automatically recognizes who the speaker is by using the speaker's speech features included in speech signal. After verifying the speaker claimed to be, it allows and enable access control of various voice services. The main applications of speaker recognition are in the field of forensic and providing additional security layer where security is the primary concern. The aim of this work is to verify a speaker with the approach of MFCC and Back Propagation Neural Network. Training function Lavenberg-Marquardt is used to train the network. Voice samples from a group of ten people uttering the same sentence five times repeatedly are collected to train the neural network. The testing of the network for verifying the speaker is done with new data set with the same utterance spoken once. A specific target or speaker ID is assigned to each speakers and verification is based on how close the network output is to the assigned code for each speaker. Verification method depends on the minimum positive error generated between the code and the actual network output. If the error is below the threshold value, the speaker claimed to be is accepted otherwise rejected. The tool for simulation is MATLAB.