Although, Linear Feedback Shift Register (LFSR) is a widely used structure in cryptography, particularly for generating Pseudo-Random Binary Sequences (PRBS) that can be used in stream ciphers. In Data Encryption Standard (DES) cryptography technique, LFSR is not a fundamental component of the technique, however, during the various processes of the DES implementation the use of LFSR are attributed in several ways to enhance cryptographic systems. In cryptographic algorithms, LFSRs can be used to generate key streams that can be XORed with plaintext. In block ciphers like DES, LFSRs can also be utilized in generating pseudo-random keys or nonces. The security of any cryptographic tool or algorithm can be influenced by the methods used for key generation. Using LFSRs for key generation, we may ensure high non-predictability of the keys. This sustainable attribute of LFSR is due to assurance of its theory governed by their mathematical models involved in the cryptographic system or algorithm. Thereby, this paper is devoted to device a mechanism to develop an LFSR based key generation scheme for DES algorithm.