We propose a computational model of recognition of the cerebral cortex, based on an approximate belief revision algorithm. The algorithm calculates the MPE (most probable explanation) of Bayesian networks with a linear-sum CPT (conditional probability table) model. Although the proposed algorithm is simple enough to be implemented by a fixed circuit, results of the performance evaluation show that this algorithm does not have bad approximation accuracy. The mean convergence time is not sensitive to the number of nodes if the depth the network is constant. The computation amount is linear to the number of nodes if the number of edges per node is constant. The proposed algorithm can be used as a part of a learning algorithm for a kind of sparse-coding, which reproduces orientation selectivity of the primary visual area. The circuit that executes the algorithm shows better correspondence to the anatomical structure of the cerebral cortex, namely its six-layer and columnar features, than the approximate belief propagation algorithm that has been proposed before. These results suggest that the proposed algorithm is a promising starting point for the model of the recognition mechanism of the cerebral cortex.