In this paper, a 4D hyperchaotic system is proposed. Some basic dynamical behaviors are explored by calculating its Lyapunov exponents, Poincar´e mapping, etc.. Finally, synchronization for this new hyperchaotic system is achieved via scalar control. The nonlinear terms in the response system are not dropped. The proposed synchronization scheme is simple and theoretically rigorous. The mathematical proof of this method is provided. Some numerical simulations are obtained. The numerical simulations coincide with the theoretical analysis.