Aiming at the leader-following consensus problem of nonlinear Markovian jumping multi-agent systems under the directed fixed topology, in order to reduce unnecessary communication between agents, save network resources and ensure system performance, an adaptive event-triggered control strategy is proposed. Firstly, each agent is taken as a Markovian jumping system, and the transition probabilities of Markov chain is partially unknown. Then, the error system is established by simple model transformation, and the consensus problem of multi-agent systems is transformed into the stability problem of the error system. On this basis, the appropriate Lyapunov-Krasovskii functional is constructed, and the sufficient conditions and the controller design method are provided for multi-agent systems to achieve leader-following consensus by using the Jensen inequality and linear matrix inequality techniques. In addition, by solving the linear matrix inequalities, the multi-agent system consensus controller gain matrices and the event-triggered parameter matrices can be obtained. Finally, the effectiveness of the proposed method is verified by numerical simulation.