In this study, we address the problem of noisy image super-resolution. Noisy low resolution (LR) image is always obtained in applications, while most of the existing algorithms assume that the LR image is noise-free. As to this situation, we present an algorithm for noisy image super-resolution which can achieve simultaneously image super-resolution and denoising. And in the training stage of our method, LR example images are noise-free. For different input LR images, even if the noise variance varies, the dictionary pair does not need to be retrained. For the input LR image patch, the corresponding high resolution (HR) image patch is reconstructed through weighted average of similar HR example patches. To reduce computational cost, we use the atoms of learned sparse dictionary as the examples instead of original example patches. We proposed a distance penalty model for calculating the weight, which can complete a second selection on similar atoms at the same time. Moreover, LR example patches removed mean pixel value are also used to learn dictionary rather than just their gradient features. Based on this, we can reconstruct initial estimated HR image and denoised LR image. Combined with iterative back projection, the two reconstructed images are applied to obtain final estimated HR image. We validate our algorithm on natural images and compared with the previously reported algorithms. Experimental results show that our proposed method performs better noise robustness.