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Abstract In this paper the synchronization of fractional-order chaotic systems and a new property of fractional derivatives are studied. Then we propose a new fractional-order extension of Lyapunov direct method to control the fractional-order chaotic systems. A new synchronization method and a linear feedback controller are given to achieve the synchronization of fractional-order chaotic systems based on a simple Lyapunov candidate function. The proposed synchronization method can be applied to the synchronization of an arbitrary fractional-order chaotic system. This method is universal, simple, and theoretically rigorous. Numerical simulations of three fractional-order chaotic systems to verify the effectiveness and the universality of the proposed method.