In mouse visual cortex, right after eye opening binocular cells have different preferred orientations for input from the two eyes. With normal visual experience during a critical period, these preferred orientations evolve and eventually become well matched. To gain insight into the matching process, we developed a computational model of a cortical cell receiving orientation selective inputs via plastic synapses. The model captures the experimentally observed matching of the preferred orientations, the dependence of matching on ocular dominance of the cell, and the relationship between the degree of matching and the resulting monocular orientation selectivity. Moreover, our model puts forward testable predictions: 1) The matching speed increases with initial ocular dominance. 2) While the matching improves more slowly for cells that are more orientation selective, the selectivity increases faster for better matched cells during the matching process. This suggests that matching drives orientation selectivity but not vice versa. 3) There are two main routes to matching: the preferred orientations either drift toward each other or one of the orientations switches suddenly. The latter occurs for cells with large initial mismatch and can render the cells monocular. We expect that these results provide insight more generally into the development of neuronal systems that integrate inputs from multiple sources, including different sensory modalities.NEW & NOTEWORTHY Animals gather information through multiple modalities (vision, audition, touch, etc.). These information streams have to be merged coherently to provide a meaningful representation of the world. Thus, for neurons in visual cortex V1, the orientation selectivities for inputs from the two eyes have to match to enable binocular vision. We analyze the postnatal process underlying this matching using computational modeling. It captures recent experimental results and reveals interdependence between matching, ocular dominance, and orientation selectivity.