In this paper, a novel synchronous policy iteration algorithm is proposed to solve the differential feedback control of the corresponding continuous-time infinite horizon linear systems. The continuous-time linear differential control problem depends on the numerical iterative solution of the related algebraic Riccati equation, which is a differential equation. Furthermore, based on reinforcement learning, the new policy iteration algorithm is executed by the structure of neural networks. And then, the evaluation neural network and the actor neural network will be constructed on the evaluator and controller respectively to complete policy evaluation and policy improvement. These two iterative steps are executed simultaneously until the overall performance of the system is stabilized. In each iterative, policy iterative algorithm is used to calculate the minimum infinite time-domain cost function associated with the updated policy. Finally, the relevant algebra Riccati equations corresponding to the system can be easily approached by the novel synchronous policy iteration algorithm. The computer simulations are given to demonstrate the feasibility and effectiveness of the novel algorithm.