For second-order leader-follower multi-agent systems with unknown nonlinear functions, an event-triggered r sliding mode control design scheme is proposed. This paper consists of two parts. In the first part, a new sliding mode reaching law based on inverse hyperbolic sine function is selected to ensure the consistency of multi-agent systems in finite time. In the second part, the sliding mode function with gain scaling factor r is designed and the event triggering mechanism is introduced. Through Lyapunov stability analysis, it is proved that the proposed control method is effective, which can not only eliminate the chattering in the system but also reduce the sampling frequency of the control action. In addition, the minimum lower bound of the triggering time interval is proved, which excludes Zeno phenomenon. Finally, the effectiveness of the proposed algorithm is verified by Matlab/simulink simulation results.