In this paper, the robust finite-time passivity for a class of fractional-order neural networks with uncertainties is considered. Firstly, the definition of finite-time passivity of fractional-order neural networks is introduced. Then, by using finite-time stability theory and linear matrix inequality approach, new sufficient conditions that ensure the finite-time passivity of the fractional-order neural network systems are derived via linear matrix inequalities which can be effectively solved by various computational tools. Finally, three numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.