A new method for finding the network coefficients of a discrete-time cellular neural network (DTCNN) is proposed. This new method uses a probabilistic approach that itself uses Bayesian learning to estimate the network coefficients. A posterior probability density function (PDF) is composed using the likelihood and prior PDFs derived from the system model and prior information, respectively. This posterior PDF is used to draw samples with the help of the Metropolis algorithm, a special case of the Metropolis-Hastings algorithm where the proposal distribution function is symmetric, and resulting samples are then averaged to find the minimum mean square error (MMSE) estimate of the network coefficients. A couple of image processing applications are performed using these estimated parameters and the results are compared with those of some well-known methods.