Super resolution (SR) image reconstruction has attracted increasing attention these years and many SR image reconstruction algorithms have been proposed for restoring a high-resolution image from one or multiple low-resolution images. However, how to objectively evaluate the quality of SR reconstructed images remains an open problem. Although a great number of image quality metrics have been proposed, they are quite limited to evaluate the quality of SR reconstructed images. Inspired by this, this paper presents a blind quality index for SR reconstructed images using first- and second-order structural degradation. First, the SR reconstructed image is decomposed into multi-order derivative magnitude maps, which are effective for first- and second-order structural representation. Then, log-energy based features are extracted on these multi-order derivative magnitude maps in the frequency domain. Finally, support vector regression is used to learn the quality model for SR reconstructed images. The results of extensive experiments that were conducted on one public database demonstrate the superior performance of the proposed method over the existing quality metrics. Moreover, the proposed method is less dependent on the number of training images and has low computational cost.