Abstract: In this paper, the Alpha-stable distribution and its fractional low order statistics are introduced. An array configuration is devised and a new method based on phase fractional lower-order moment (PFLOM) is proposed for 2-D direction of arrival (DOA) estimation. PFLOM-based covariance matrix of the desired signal can be derived from that of the receive signal. Making use of eigenvalue decomposition and applying least square or total least square method, we can derive DOA. Finally, the ESPRIT methods based on classic covariance matrix, SCM, FLOM, and PFLOM are compared in this paper. Simulations show that the method has robust performance and the smaller bias and mean square errors.