Abstract: This paper studies the robust finite-time stability problem for nonlinear conformable fractional-order impulsive systems with time delay under external disturbances. The method adopts the conformable fractional derivative framework, combines the Lyapunov method, considers the coupling effects of impulsive effects and time delay, derives the criteria for the system to achieve robust finite-time stability, and obtains the corresponding stability time. The effectiveness of the proposed theoretical results is verified through Matlab-based numerical simulation examples. The results show that in the simulation of a one-dimensional system with \alpha =0.97 , the system stability time is 7.28 s without impulses, which is reduced to 5.858 s under the action of 3 stable impulses and further shortened to 3.794 s with 6 stable impulses. In contrast, the system stability time increases to 16.796 s under the action of unstable impulses, and the system with unstable impulses can still achieve finite-time stability when the robust conditions are satisfied. This study obtains new results on the robust finite-time stability of nonlinear conformable fractional-order impulsive systems with time delay, clarifies the different regulatory rules of impulsive effects on the system's convergence process and stability time, and reveals the stability characteristics of the system under the coupling effects of impulses, time delay, and disturbances.