Contour detection is a salient operation in many computer vision applications as it extracts features that are important for distinguishing objects in scenes. It is believed to be a primary role of simple cells in visual cortex of the mammalian brain. Many of such cells receive push-pull inhibition or surround suppression. We propose a computational model that exhibits a combination of these two phenomena. It is based on two existing models, which have been proven to be very effective for contour detection. In particular, we introduce a brain-inspired contour operator that combines push-pull and surround inhibition. It turns out that this combination results in a more effective contour detector, which suppresses texture while keeping the strongest responses to lines and edges, when compared to existing models. The proposed model consists of a Combination of Receptive Field (or CORF) model with push-pull inhibition, extended with surround suppression. We demonstrate the effectiveness of the proposed approach on the RuG and Berkeley benchmark data sets of 40 and 500 images, respectively. The proposed push-pull CORF operator with surround suppression outperforms the one without suppression with high statistical significance.