In this work, we propose a telegraph coupled partial differential equation (TCPDE) based model for image restoration. The new framework interpolates between a couple of nonlinear telegraph equation and a parabolic equation. This proposed strategy can be applied to significantly preserve the oscillatory and texture pattern in an image, even in low signal-to-noise ratio (SNR). First, we prove that the present model has a unique global weak solution using Banach’s fixed point theorem. Then we apply our model over a set of gray level images to illustrate the image denoising ability of the proposed model. The experimental results of the proposed model are reported, which found better in terms of noise elimination and edge preservation, with respect to the recently developed hyperbolic–parabolic PDE based models as well as coupled diffusion-based model.