In this paper, the problem of robust fixed-time trajectory tracking control for a class of nonlinear Euler-Lagrange (EL) systems with exogenous disturbances and uncertain dynamics is addressed. A neural network (NN)-based adaptive estimation algorithm is employed to approximate the continuous uncertain dynamics, so that the dynamics of the EL system can be rebuild based on the estimations. In order to guarantee the EL system following the desired trajectory within a fixed-time, an adaptive fixed-time sliding mode control law is proposed to remedy the negative influence of uncertain dynamics and exogenous disturbances. Lyapunov stability theory is utilized to prove the stability and fixed-time convergence of the EL system. The efficiency of the developed NN-based adaptive fixed-time control strategy is substantiated with simulation results.