Random unique number generator can be used for generating a series of unpredictable and unrepeatable numbers within limited ranges of data and numbers. These numbers are usually distributed equally, random, independent, unpredictable and unrepeatable. A good random number generator has to be effective for a long period and has good statistical distribution and efficient generating performance. This study proposes a computational methodology to generate pseudo-random numbers based on random base polynomial, which uses less memory but generates a great deal of unrepeated pseudo-random numbers. Then this method adopts the multi-thread parallelization to effectively get the benefits of multi-core processors to accelerate the generation of a huge amount of pseudo-random numbers.