Noisy image super-resolution (SR) is a significant challenging process due to the smoothness caused by denoising. Iterative back-projection (IBP) can be helpful in further enhancing the reconstructed SR image, but there is no clean reference image available. This paper proposes a novel back-projection algorithm for noisy image SR. Its main goal is to pursuit the consistency between LR and SR images. We aim to estimate the clean reconstruction error to be back-projected, using the noisy and denoised reconstruction errors. We formulate a new cost function on the principal component analysis (PCA) transform domain to estimate the clean reconstruction error. In the data term of the cost function, noisy and denoised reconstruction errors are combined in a region-adaptive manner using texture probability. In addition, the sparsity constraint is incorporated into the regularization term, based on the Laplacian characteristics of the reconstruction error. Finally, we propose an eigenvector estimation method to minimize the effect of noise. The experimental results demonstrate that the proposed method can perform back-projection in a more noise-robust manner than the conventional IBP, and harmoniously work with any other SR methods as a post-processing.