This paper proposes a new model-free event-triggered optimal control algorithm for continuous-time linear systems. The problem is formulated as an infinite-horizon optimal adaptive learning problem, and we are able to simultaneously address the issue of designing a control and a triggering mechanism with guaranteed optimal performance by design. In order to provide a model-free solution, we adopt a Q-learning framework with a critic network to approximate the optimal cost and a zero-order hold actor network to approximate the optimal control. Since we have dynamics that evolve in continuous and discrete-time, we write the closed-loop system as an impulsive model and prove asymptotic stability of its equilibrium. Numerical simulation of an unknown unstable system is presented to show the efficacy of the proposed approach. (C) 2017 Elsevier Ltd. All rights reserved.