This paper discusses pseudo-randomness of a periodic sequence, named the fourth class of GSS sequence. We get the following results: ① Its least period always reaches the maximum (that is, 2n-1). ② Its least period and linear complexity keep robust under single-symbol-substitution. ③ It has good low-degree-auto-correlation feature. ④ It has good short-length-run-distribution. This paper discusses the pseudo-randomness of a periodic sequence, named the fourth class of GSS sequence. We get the following sequence: ① The least period always reaches the maximum (that is, 2n-1). robust under single-symbol-substitution. ③ It has good low-degree-auto-correlation feature.