Poisson noise is a common electronic noise, which has widely occurred in various photo-limited imaging systems. However, due to signal-dependent and multiplicative characteristics for Poisson noise, Poisson denoising is still an open problem. In this paper, we propose a novel approach using simultaneous nonlocal low-rank and deep priors (SNLDP) for Poisson denoising. The proposed SNLDP simultaneously employs nonlocal self-similarity and deep image priors under the hybrid plug and play framework, which comprises multiple pairs of complementary priors, namely, nonlocal and local, shallow and deep, and internal and external. To make the optimization tractable, an effective alternating direction method of multiplier (ADMM) algorithm under the alternative minimization framework is provided to solve the proposed SNLDP-based Poisson denoising problem. Experimental results demonstrate the superiority of the proposed SNLDP over many popular or state-of-the-art Poisson denoising algorithms in terms of quantitative and visual perception.