This paper investigates the globally and exponentially consensus problem for a kind of multi-agent systems with discontinuous dynamics and hybrid self-delays. Through implementing distributed negative feedback control strategy with time-varying control gain, the communication of state information among agents is achieved. Since it is impossible for the amplitude of the control signal that reaches infinite in practical applications, the saturation strategy is utilized to limit the control effect into certain reasonable ranges. In order to reduce the non-smoothness of control signal, the Gaussian error function and the differential mean value theorem are jointly taken to simulate the saturation effect. Furthermore, the Filippov differential inclusion and the measure selection theorem are utilized to deal with discontinuous differential equations. Then the exponentially consensus criteria and the admissible delay are derived by applying the generalized Halanay inequality and the Lyapunov stability theorem. Finally, the effectiveness of the proposed control strategy is verified by numerical simulation.