Convolutional Neural Network (CNN) are popular to model object recognition in the brain. They offer a flexible and convenient framework to model the hierarchical stacking of cortical areas that compose the Visual Ventral Stream. However, CNN suffers from major drawbacks in comparison with realistic models of biological vision. First, CNN are mostly feedforward and cannot account for the recurrent processing that takes place in the visual cortex. Second, the back-propagation rule used to train CNN involves global learning rules unlikely to be implemented in the brain. Third, the representation generated by CNN are most often dense whereas those generated by the visual cortex are sparse. To address these problems we propose a new model called Sparse Deep Predictive Coding (SDPC). The SDPC framework takes advantage of the Predictive Coding (PC) theory to model the dynamic update scheme observed in the visual cortex. PC suggests, among other scenarios, that feedback connections from a higher cortical area carry neural predictions to the lower cortical area, while the feedforward connections propagates the unpredicted information (or prediction error) to the higher area. As such, the neuronal state of a layer is recursively updated towards minimized prediction error. Interestingly, PC approximates the CNN back-propagation into a local learning rule that is assimilable to a biologically realistic Hebbian learning rule. Last but not least, PC includes a local competition mechanism between neurons that performs an `explaining away’ strategy thought sparse coding. The SDPC offers a hierarchical and convolutional implementation of the PC theory. We experimentally assess the SDPC model using two different image databases. First, we quantify how well the SDPC is untangling the visual information contained in the MNIST database (handwritten digits) under normal and noisy condition. To do so, we train a simple linear classifier to recognize SDPC representation, and we assess the classification accuracy with different level of perturbation. Our results show that the SDPC compete with similar state-of-the-art model in term of classification accuracy and noise robustness. Second, we point out the qualitative similarities between the biological Receptive Fields (RFs) of the early visual cortex and the features learnt by the SDPC model on a face database (AT&T). As a result the SDPC model accounts both for high level behavioral observation (recognition under noisy and normal environment) and electrophysiological results (Gabor-like RFs).