Linear Feedback Shift Register based Unique Random Number Generator is an enhancement of Random Number generator with the additional property that any number generated by a unique random number generator can’t be duplicated. As per users demand for not duplicated random numbers in some applications like transferring a random number over the network on the behalf of actual character of the message for security point of view, existence of unique random number generators are very essential. In this paper LFSR [1] (Linear Feedback Shift Register) is used to implement the proposed concept of unique random number generator. Using LFSR is a faster approach for generating random sequences because it requires only X-OR operations and shift registers that’s why its implementation is very easy in software as well as in hardware [2, 3]. We can easily modify the LFSR and produce different random sequences. So it is the best option for using LFSR in unique random number generator.