Based on the ideas of E.N. Sokolov about the mechanisms of the “vector encoding” information in the brain the spherical connectionist model of visual cognitive action was constructed. This model takes into account and expressed in mathematical form some neurophysiological data on the structure and functioning of the real neural networks of the brain. In this model, using the general principles of “vector coding”, all the main stage cognitive action have been described in a mathematical form, including the step of exposing the object on the retina and the step of evaluating the correctness of the response to a stimulus. Psychophysiological problem has also been considered. The transition of the perceived object from his physiological state F at the output of pre-detectors to unconsciously perceived (psychological) state D at the output of the ensemble detectors and the model awareness of sensations of the object properties has been described. The developed spherical connectionist model of cognitive actions allowed uniting in the activity psychology the ideas of E.N. Sokolov about the “vector coding” of the object properties in the brain and the A.N. Leontiev’s ideas about the mechanisms of “active psychic reflection of the object by the subject”.