Because the high quality pseudo-random numbers are important in the field of cryptography,a new pseudo-random numbers generator based on 2-by-n Cellular Automata (CA) was proposed.Focused on maximum period,the corresponding rule in CA was firstly discussed. Then it was introduced in detail on how to get maximum period in the new generator. Furthermore, the structure of the new generator was explored.At last, the generated numbers was tested according to the standard of FIPS 140 2 statistical tests for randomness.And the results indicated that the generator can generate the high-quality pseudo-random numbers,which have good statistical properties and can be applied in cryptography.