© 2022 IEEE.Magnetic resonance imaging (MRI) reconstruction is one of the important inverse imaging problems. Unlike the classical MRI approaches which demand long scanning time and are prone to reconstruction artifacts, compressed sensing MRI (CS-MRI) generates the scans data relatively faster and produces less artifacts for medical diagnosis. Model-based CS-MRI algorithms require long reconstruction time to obtain an MR image. On the other hand, although training time of deep learning techniques for the task is rather long, their reconstruction time is much shorter compared to iterative model-based MRI algorithms. Moreover, recent works have shown that Gaussian denoisers including deep denoisers can be utilized to solve the inverse problems in a plug-and-play fashion. In this paper, we propose an iterative convolutional neural network based Gaussian denoiser as a solver for the CS-MRI problem. Our experiments show that the proposed method has better reconstruction ability when compared to some important model-based and deep learning based methods from the literature.