The size of a neuron's receptive field increases along the visual hierarchy. Neurons in higher-order visual areas integrate information through a canonical computation called normalization, where neurons respond sublinearly to multiple stimuli in the receptive field. Neurons in the visual cortex exhibit highly heterogeneous degrees of normalization. Recent population recordings from visual cortex find that the interactions between neurons, measured by spike count correlations, depend on their normalization strengths. However, the circuit mechanism underlying the heterogeneity of normalization is unclear. In this work, we study normalization in a spiking neuron network model of visual cortex. The model produces a range of neuronal heterogeneity of normalization strength and the heterogeneity is highly correlated with the inhibitory current each neuron receives. Our model reproduces the dependence of spike count correlations on normalization as observed in experimental data, which is explained by the covariance with the inhibitory current. We find that neurons with stronger normalization are more sensitive to contrast differences in images and encode information more efficiently. In addition, networks with more heterogeneity in normalization encode more information about visual stimuli. Together, our model provides a mechanistic explanation of heterogeneous normalization strengths in the visual cortex, and sheds new light on the computational benefits of neuronal heterogeneity.