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In this paper, a fractional-order hyperchaotic system is proposed. By computer simulations, it is found that hyperchaos exists in the new fractional-order four dimensional system with order less than one. Using the pole placement technique, a nonlinear state observer and is designed to synchronize a class of nonlinear fractional-order systems. In addition, the function projective synchronization between the new integer-order hyperchaotic system and the fractional-order hyperchaotic system. The two schemes, based on the stability theory of the fractional-order system, are rather simple, theoretically rigorous and convenient to realize synchronization. Numerical results are performed to verify the effectiveness of the proposed synchronization schemes.