This paper proposes a Full Range Gaussian Markov Random Field (FRGMRF) model for monochrome image compression, where images are assumed to be Gaussian Markov Random Field. The parameters of the model are estimated based on Bayesian approach. The advantage of the proposed model is that it adapts itself according to the nature of the data (image) because it has infinite structure with a finite number of parameters, and so completely avoids the problem of order determination. The proposed model is fitted to reconstruct the image with the use of estimated parameters and seed values. The residual image is computed from the original and the reconstructed images. The proposed FRGMRF model is redefined as an error model to compress the residual image to obtain better quality of the reconstructed image. The parameters of the error model are estimated by employing the Metropolis-Hastings (M-H) algorithm. Then, the error model is fitted to reconstruct the compressed residual image. The Arithmetic coding is employed on seed values, average of the residuals and the model coefficients of both the input and residual images to achieve higher compression ratio. Different types of textured and structured images are considered for experiment to illustrate the efficiency of the proposed model. The results obtained by the FRGMRF model are compared to the JPEG2000. The proposed approach yields higher compression ratio than the JPEG whereas it produces Peak Signal to Noise Ratio (PSNR) with little higher than the JPEG, which is negligible.