The Cell-Free mMIMO networks can provide a satisfied performance for 5G networks and beyond even there are shadowed users or indoor ones. The performance of cell-Free mMIMO networks was mathematically analyzed and simulated. This work aims to apply the cognitive relays in cell-Free mMIMO networks. The cell-Free mMIMO system, based on cognitive relays, is mathematically analyzed and simulated. The proposed work depends on two axes. Firstly, the relays can improve the performance of cell-Free mMIMO networks especially at shadowed users and cell-edge ones. Secondly, the cognitive radio can mitigate the interference in a cell-Free mMIMO network. The Cell-Free mMIMO network, based on cognitive relays, is proposed. The system is mathematically analyzed and simulated. The spectral efficiency SE and signal to interference plus noise ratio SINR is deduced and given in a closed form formula. It can be concluded that the cognitive relays can improve; SINR, SE, and Energy Efficiency EE of a cell-Free mMIMO network.