We present a new approach to edge detection on synthetic aperture radar (SAR) images based on contourlet-domain hidden Markov tree (CD-HMT) model. In the contourlet transform, a double filterbank structure, pyramidal directional filterbank, is employed by first using Laplacian pyramidal decomposition and then a local directional filterbank. Compared with the wavelet transform, the contourlet transform not only can capture multiresolution and local information of an image, but obtain its directional information in a flexible way by using different number of directions at different scales. This non-separable two-dimensional transform is a new alternative to and improvement on separable wavelets for the representation of an image. On the other hand, HMT is a tree-structured probabilistic graph that can capture the statistical properties of contourlet coefficients at different scales and directions where each coefficient is considered as an observation of its hidden state variable which indicates whether the coefficient belongs to singularity structures or not. Herein, the state "1" represents the location belonging to singularity structure, and state "0" not. CD-HMT model is firstly trained by Expectation-Maximization (EM) algorithm before the Viterbi algorithm is utilized to uncover the hidden state sequences based on maximum a posterior (MAP) estimation. Moreover, we take into account the effect of speckle on the detection performance for singularity structures. Finally, the thinning post-processing procedure is performed to obtain the edge map of an SAR image. Experiments on both simulated speckled and real SAR images demonstrate the feasibility and effectiveness of our approach with the performance outperforming the classical Canny edge detector.