Random numbers play a crucial role in modern security schemes. Couple to the rapid development of cryptography, the strength of security protocols and encryption algorithms consumingly relies on the quality of random number. With simple architecture and faster speed, linear feedback shift register often is selected in many applications. However, the random sequence generated by LFSR can not meet the demand of unpredictability for secure mechanism. Genetic algorithm improves the linear property of LFSR and constructs a novel random sequence generator with longer period and complex architecture.With the development of cryptography, the need for random numbers of high quality is sharply growing. Public/private keypairs for asymmetric algorithms are generated from random bit streams [1,2] ; random numbers are also used for key generation in symmetric algorithms for generating challenges in authentication protocols to create padding bytes and blinding values [3] . In the Smart Card, countermeasures against side-channel attacks can also require the availability of good quality random number source [4] . The security of many cryptographic systems depends on the assumption that future values in the random sequence can be unpredictable [5] .Linear feedback shift registers (LFSR) are one class of generators for random sequence, and are suited to low power or high speed requirements [6] . LFSR sequence are not considered on their own to provide an adequate strength random bit stream because the dependency between the output bits and the inner state can be modeled by a system of linear equations. However, LFSR is a useful building block for pseudo random number generation when complemented by further complexity to prevent attacks based on its inherent linearity. From a hardware perspective, LFSR can be created by using a chain of flip-flops.It is well known that genetic algorithm possess very interesting function approximation capabilities [7,8] . Their most important and intriguing property are their optimization capabilities. This operation is also a kind of nonlinear operation, which is needed in the nonlinear design of LFSR. In this paper, exploiting genetic algorithm, a novel random bit sequence based on LFSR is constructed.