In this paper, Universal Learning Networks with Branch Control (BrcULNs) are proposed, which consist of basic networks and branch control networks. The branch control network can be used to determine which branches of the basic network should be connected or disconnected. This determination depends on the inputs or the network flows of the basic network. Therefore, by using the BrcULNs, locally functions distributed networks can be realized depending on the values of the inputs of the network or the information of the network flows. The proposed network is applied to some function approximation problems. The simulation results show that the BrcULNs exhibit better performance than the conventional networks with comparable complexity.