In this paper, the leader-follower fixed-time consensus problem of networked nonlinear multi-agent systems (NNMASs) with unknown disturbance is investigated. A new event-triggered super-twisting fixed-time sliding mode consensus control (ESFSMCC) method is proposed, enabling all agents to achieve consensus in a fixed time. Firstly, a terminal sliding mode variable is designed to eliminate the convergence time dependence on the initial values of the system and avoid singularity. Secondly, a distributed event-triggered mechanism is developed to effectively reduce inter-agent communication frequency in a networked environment. In contrast to the existing fixed-time consensus control method, the improved super-twisting algorithm is adopted to construct a control protocol to achieve both global fixed-time consensus robustness and alleviate the issue of high-frequency chattering. Thirdly, the Lyapunov theory is utilized without the piecewise sliding mode technique to derive sufficient conditions for establishing the fixed-time stability of NNMASs, which still avoids the singularity problem. In this paper, the non-segmented terminal sliding mode is employed to prove the global fixed-time stability of the system states, thereby avoiding computational complexity. Finally, the effectiveness and advantages of the proposed method are verified through numerical simulations.