Trinomial property of p-ary periodic sequences generated by trace function are discussed using the theory of trace function over finite field in this paper.Some necessary and sufficient conditions for trinomial property of p-ary sequences generated by trace function of period p

n

1 as well as conditions of the equivalent trinomial pairs and classifications for trinomial pairs are point out（regular and nonregular trinomial pairs）.And using the trace representation of the sequences

by different methods

we prove that the p-ary GMW and cascaded p-ary GMW sequences have regular trinomial property

and give the corresponding regular trinomial pairs.