Synthetic aperture radar (SAR) can provide stable data source for earth observation due to its advantages of all day and night, all-weather, and strong penetration. SAR image classification as a fundamental procedure has been proved its great value in plenty of remote sensing applications. Conventional classification algorithms mainly rely on hand-designed features, which are susceptible to widespread coherent speckle noise and geometric distortion in high-resolution SAR images. Inspired by the recent impressive success in data mining and deep learning, a greedy hierarchical convolutional neural network (GHCNN) is developed. It aims at obtaining optimized feature representation, relieving the effect of speckle noise, and promoting the local pattern recognition of geometric distortion in single-polarized SAR image classification. First, a series of convolutional autoencoders (CAEs) is trained in the greedy layer-wise unsupervised strategy. This step provides an unbiased regularizer and <i>a priori</i> distribution derived from large volumes of unlabeled SAR patches. Then, to optimize multiple parameter subspaces globally, several CAEs are coupled together to form a deeper hierarchical structure in a stacked and unsupervised fashion. Afterward, a convolutional network with identical topology inherits the pretrained weights. After supervised finetuning, it realizes class prediction. Synchronously, t-distributed stochastic neighbor embedding (t-SNE) algorithm is applied to monitor the efficiency of feature representation during the training period. Experimental results demonstrate that the proposed method has competitive advantages over involved contrast methods.