Binary sequences with large linear complexity have been found many applications in communication systems.We determine the linear complexity of a family of p~2-periodic binary sequences derived from polynomial quotients modulo an odd prime p.Results show that these sequences have high linear complexity,which means they can resist the linear attack method. Binary sequences with large linear complexity have been found many applications in communication systems. We determine the linear complexity of a family of p ~ 2-periodic binary sequences derived from polynomial quotients modulo an odd prime p. Results show that these sequences have high linear complexity , which means they can resist the linear attack method.