Abstract: In view of the time difference between two sensors caused by arriving signals early or late from the same source,a quaternion signal model using two sensors’ signals is established,and a Toeplitz matrix of that quaternion model is constructed.After analyzing the Toeplitz matrix,an estimation algorithm is presented.Finally,the right-eigenvalue decomposition of the quaternion matrix is used to construct a corresponding noise subspace and then a quaternion-MUSIC method is used to estimate time-delay when signal frequency is known.Simulation illustrates that the proposed method is effective.