The paper implements the research of spatial spectrum estimation for coprime linear array. By utilizing the conjugate augmented characteristic of the second-order statistic of the signals, a conjugate augmented unitary estimation of signal parameters via rotational (ESPRIT) (CA-UESPRIT) direction of arrival (DOA) estimation algorithm is proposed. By using the second-order statistics of the received signals with different time lags, the algorithm firstly constructs a conjugate augmented virtual array to expand the array aperture and improve degrees of freedom (DOFs), subsequently, achieves the DOA estimation by exploiting the coprime property based joint UESPRIT algorithm. Compared to the traditional joint UESPRIT algorithm for coprime linear array, better DOA estimation performance can be achieved by CA-UESPRIT algorithm. In addition, the covariance matrix of the ESPRIT algorithm can be transformed from the complex domain to the real domain by the unitary transform, which reduces the complexity but ensures the estimation accuracy. The simulation results verify the effectiveness of the proposed algorithm.