Synthetic aperture radar (SAR) images are contaminated by speckle noise, which has largely limited its practical applications. Recently, convolutional neural networks (CNNs) have indicated good potential for various image processing tasks. In this paper, we propose a self-calibrated convolutional neural network for SAR image despeckling, called SAR-SCCNN. To enlarge the receptive field of the network, downsampling and dilated convolutions are employed in each self-calibrated block. Also, the contextual information from spaces with different scales is extracted and concentrated to obtain accurate despeckled images. Experiments on synthetic speckled and real SAR data are conducted to perform the subjective visual assessment of image quality and objective evaluation. Results show that our proposed method can effectively suppress speckle noise and preserve detailed features.