This paper deals with the finite-time stability problem of non-linear singular multi-agent systems subject to controller gain disturbance via a distributed non-fragile controller. The existing literature on this problem only applies to normal multi-agent systems, or ignores the possible change of control gain in the practical application of the controller, or requires that there is no time-varying delay in the control input. How to tackle the finite-time stability problem of singular multi-agent systems by considering input time-varying delay, Lipschitz non-linear dynamics and controller gain perturbation simultaneously is an open issue. In order to solve this problem, a distributed non-fragile controller is proposed for each agent to make the finite-time stability problem solved for any connected undirected connection topology. With the help of a Linear matrix inequality and a Lyapunov integral appropriate expression, the difficulty caused by the irreversibility of singular system matrices is solved. Then, a sufficient condition to ensure the finite-time stability of the closed-loop system is obtained for the singular multi-agent system including controller disturbance, input-output delay and non-linear dynamics. Finally, two numerical examples are used to illustrate the effectiveness of the proposed method.