In this paper, based on the stability theory of the fractional-order system, an idea of using state observer to realize the full-state projective synchronization of fractional-order chaotic system is proposed. The designed observer can achieve full-state projective synchronization in a class of nonlinear fractional-order systems without the limitation of partial-linearity, extend the scope of application of projective synchronization, and does not require the calculation of the conditional Lyapunov exponents. In addition, this synchronization method is simple and theoretically rigorous, capable to achieve a full-state synchronization of arbitrary scaling factor. Finally, the method has been applied to realize the full-state projective synchronization of fractional-order Rssle system, and the simulation results verified the effectiveness of the method.