We propose a computational model of push-pull inhibition (ON inhibition in OFF subfields and vice-versa) of simple cells. It is based on an existing orientation-selective model called Combination of Receptive Fields (CORF), which combines, by an AND-type operation, the responses of model LGN cells with appropriately aligned center-surround receptive fields. A push-pull response is computed as the response of a CORF model cell that is selective for a stimulus with preferred orientation and contrast minus a fraction of the response of a CORF model that responds to the same stimulus but of opposite contrast. The proposed push-pull model exhibits an improved signal-to-noise ratio and achieves two properties that are observed in real simple cells: contrast-dependent changes in spatial frequency tuning and separability of spatial frequency and orientation. For two benchmark data sets (RuG: 40 images, Berkeley: 500 images), we demonstrated that the proposed push-pull model outperforms (with very high statistical significance) the Gabor function model with (and without) surround suppression and Canny contour detector. The push-pull model that we propose contributes to a better understanding of how the brain processes visual information and is highly effective in edge detection, which is considered as the primary biological role of simple cells.