This article emphasizes the finite‐time state estimation problem for delayed complex dynamical networks with random parameters. In order to reduce the amount of transmission process, an aperiodic sampled‐data event‐triggered mechanism is introduced to determine whether the measurement output should be released at certain time points which incorporate an appropriate triggering condition and sampling moments. Furthermore, a concept of finite‐time boundedness in the pth moment is proposed to access the performance of state estimator. The objective of this article is to design an event‐triggered state estimator to estimate the states of nodes such that, in the presence of time delays, uncertainties, and randomly changing coupling weights, the estimation error system is finite‐time bounded in the pth moment related to a given constant. Some sufficient conditions in form of linear matrix inequalities and algebraic inequalities are established to guarantee finite‐time boundedness. Finally, a numerical example is presented to show the effectiveness of the theoretical results.