Abstract: In this paper we give a preconditioned conjugate gradient method(PCG)to solve the Hermitian To-eplitz system Ax=b.Based on the fact that an Hermitian Toeplitz matrix Acan be reduced into a real Toeplitzmatrix plus a Hankel matrix(i.e.,UAU*=T+H)by a unitary similarity transformation(this unitary matrix  is U=(I-iJ)/ √2),we first reduce the system Ax=b to a real linear systems(T+H)[x1,x2]=[b1,b2]. Then we propose a new preconditioner for solving those two systems.In particular,our solver only involveseal arithmetics when the discrete sine transform(DST)and discrete cosine transform(DCT)are used.The  spectral properties of the preconditioned matrix are analyzed,and the computational complexity is discussed. Numerical experiments show that our preconditioner performs well for solving the Hermitian Toeplitz systems.

Key words: Hermitian Toeplitz matrix , PCG, DST, DCT