Recurrent neural networks are proposed to synthesize linear control systems through pole placement (assignment). The proposed neural network approach uses two coupled recurrent neural networks to compute a feedback gain matrix. Each neural network consists of two bidirectionally connected layers and each layer consists of an array of neurons. The proposed recurrent neural networks are shown to be capable of synthesizing linear control systems in real time. The operating characteristics of the recurrent neural networks and closed-loop systems are demonstrated by use of three illustrative examples.