The hardware random number generator is a source of unpredictable, statistically random stream sequences. Critical cryptography applications require the production of an unpredictable and unbiased stream of binary data derived from a fundamental noise mechanism. In this paper, we analyzed hardware random number generator with Gaussian noise using randomized algorithm in respect of security consideration. In this paper, hardware random number system on embedded Linux on chip (LOC) processor, MC68328, is reviewed to reduce the statistical property of the biased bit stream in the output of a random number generator. In experiments of the randomness evaluation for the randomized algorithm, we evaluated the statistical evaluation for 10 test samples, the severe biased and the moderate biased stream. Although the random bit stream has the biased characteristics. But the differential quantities are compensated using the randomized process by chaos function. Therefore in the randomness evaluation of hardware generator, the proposed randomized algorithm is always satisfied the randomness test condition.