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Recent success in the field of single image super-resolution (SISR) is achieved by optimizing deep convolutional neural networks (CNNs) in the image space with the L1 or L2 loss. However, when trained with these loss functions, models usually fail to recover sharp edges present in the high-resolution (HR) images for the reason that the model tends to give a statistical average of potential HR solutions. During our research, we observe that gradient maps of images generated by the models trained with the L1 or L2 loss have significantly lower variance than the gradient maps of the original high-resolution images. In this work, we propose to alleviate the above issue by introducing a structure-enhancing loss function, coined Gradient Variance (GV) loss, and generate textures with perceptual-pleasant details. Specifically, during the training of the model, we extract patches from the gradient maps of the target and generated output, calculate the variance of each patch and form variance maps for these two images. Further, we minimize the distance between the computed variance maps to enforce the model to produce high variance gradient maps that will lead to the generation of high-resolution images with sharper edges. Experimental results show that the GV loss can significantly improve both Structure Similarity (SSIM) and peak signal-to-noise ratio (PSNR) performance of existing image super-resolution (SR) deep learning models.