Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd（p-1, q-1 ）=gcd（p- 1, r-1）=gcd（q-1, r-1）=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF（2） is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.
