This paper addresses an H∞ control approach on neural networks with hybrid-triggered mechanism (HTM) under deception attacks. With the aim of mitigating the burden of the transmission network, an HTM is introduced to handle unforeseen non-ideal environment influence, which is characterized by Bernoulli distribution. The weight combination coefficients ϵj related to historical information are conducted to develop an improved HTM. By taking into account network-induced delay, and the randomly happened deception attacks in transmission network, a Lyapunov–Krasovskii functional (LKF) is constructed. Using linear matrix inequality (LMI), sufficient conditions are formed to render the system asymptotically stable and the H∞ hybrid-triggered controller is designed. Finally, simulation examples are executed to validate the feasibility of the developed method.