To date, Hebbian learning combined with some form of constraint on synaptic inputs has been demonstrated to describe well the development of neural networks. The previous models revealed mathematically the importance of synaptic constraints to reproduce orientation selectivity in the visual cortical neurons, but biological mechanisms underlying such constraints remain unclear. In this study, we addressed this issue by formulating a synaptic constraint based on activity-dependent mechanisms of synaptic changes. Particularly, considering metabotropic glutamate receptor-mediated long-term depression, we derived synaptic constraint that suppresses the number of inputs from individual presynaptic neurons. We performed computer simulations of the activity-dependent self-organization of geniculocortical inputs with the synaptic constraint and examined the formation of receptive fields (RFs) of model visual cortical neurons. When we changed the magnitude of the synaptic constraint, we found the emergence of distinct RF structures such as concentric RFs, simple-cell-like RFs, and double-oriented RFs and also a gradual transition between spatiotemporal separable and inseparable RFs. Thus, the model based on the synaptic constraint derived from biological consideration can account systematically for the repertoire of RF structures observed in the primary visual cortices of different species for the first time.