In this paper, we provide a new iterative algorithm via the weighted low-rank tensor model for Poisson image denoising. The noise variance of the scaled Poisson data is transformed at each iteration through the Anscombe transformation obtaining a signal where the noise is as additive white Gaussian noise. Then this Gaussian noise is removed using the weighted low-rank tensor filter with the local and nonlocal geometry information because of natural images containing patches with high similarity. Finally, an exact unbiased inverse is constructed to estimate the signal of interest. Experimental results demonstrate the superior performance of our proposed method compared with other Poisson denoising algorithms on the ten test images.