In this work, we study the fixed-time stability of fractional-order systems. By virtue of the properties of Riemann-Liouville fractional derivative and the comparison principle, we derive a new fixed-time stability theorem for fractional-order systems. Meanwhile, order-dependent setting time is formulated. Based on the developed fixed-time stability theorem, a fixed-time synchronization criterion for fractional-order neural networks is given. Simulation result demonstrates the effectiveness of our proposed results.