Abstract: ‍ ‍This study proposes a two-dimensional direction-of-arrival （DOA） estimation method of virtual conjugate interpolation for an L-shaped coprime array to address the issue of existing DOA estimation methods， which cannot make full use of the discontinuous array element information and signal time domain information， leading to low DOA estimation accuracy， a small array aperture， and limited degrees of freedom. The method is first based on the received array data of the L-shaped coprime array. The received data matrix of the virtual conjugate augmented array is constructed by calculating its cross-correlation function. Then， by utilizing array interpolation zero-padding and selecting the non-zero columns of the covariance matrix， the received data matrix of the virtual uniform linear array with partially missing terms is obtained， and by the idea of atomic norms， the gridless convex optimization problem is constructed， the missing terms of the virtual uniform line array covariance matrix are filled， and the estimated values of the angles between the incoming signals and the x- and z-axis positive directions are obtained by using the root multiple signal classification method. Finally， based on the uniqueness of the virtual source power， the estimated angles of each axis are matched by constructing the relevant cost function， and then the azimuth and elevation angles are estimated and matched according to the relationship between the angle of each axis and the azimuth and elevation angles. This method improves the accuracy of DOA estimation， expands the array aperture， increases the degree of freedom， and reduces the computational complexity using the root multiple signal classification method. The simulation results show that the method proposed in this study can achieve two-dimensional DOA estimation and angle matching， and compared to the comparison method， the proposed method can estimate more signal sources and has better DOA estimation performance.