This paper presents the theoretical results on sliding mode control (SMC) of neural networks via continuous or periodic sampling event-triggered algorithm. Firstly, SMC with continuous sampling event-triggered scheme is developed and the practical sliding mode can be achieved. In addition, there is a consistent positive lower bound for the time interval between two successive trigger events which implies that the Zeno phenomenon will not occur. Next, a more economical and realistic SMC technique is presented with periodic sampling event-triggered algorithm, which guarantees the robust stability of the augmented system. Finally, two illustrative examples are presented to substantiate the effectiveness of the derived theoretical results.