Abstract: To improve the estimation accuracy of angles and ranges of near-field source while reducing computational complexity, this paper proposes a near-field source localization method based on covariance fitting. First, by calculating the spatial correlation functions between symmetric array elements, the angle and range information of near-field source is decoupled. Then, the covariance matrix is obtained via spatial smoothing. Subsequently, based on a covariance fitting criterion with a rank constraint, the covariance matrix is reconstructed by solving a corresponding semidefinite programming problem. Finally, the root-MUSIC method is employed to estimate the angles of near-field sources. Based on the estimated angles and the noise subspace of the array-received data covariance matrix, with the principle of the root-MUSIC method, range estimation of near-field sources is realized by solving a corresponding polynomial. Simulation results demonstrate that the proposed method improves the estimation accuracy of both angle and range for near-field sources, achieves matching between angle and range estimation, and reduces computational complexity by replacing spectral peak search with polynomial solution.