This work presents a neuroadaptive tracking control scheme embedded with memory-based trajectory predictor for Euler-Lagrange (EL) systems to closely track an unknown target. The key synthesis steps are: 1) using memory-based method to reconstruct the behavior of the unknown target based on its past trajectory information recorded/stored in the memory; 2) blending both speed transformation and barrier Lyapunov function (BLF) into the design and analysis; and 3) introducing a virtual parameter to reduce the number of online update parameters, rendering the strategy structurally simple and computationally inexpensive. It is shown that the resultant control scheme is able to ensure prescribed tracking performance in which close target tracking is achieved without the need for detailed information about system dynamics and the target trajectory; the tracking error converges to the prescribed precision set within a prespecified finite time at an assignable rate of convergence; and the full-state constraints are never violated. Furthermore, all the signals in the closed-loop system are bounded and the control action is C1 smooth. The benefits and feasibility of the developed control are also verified and confirmed by simulation.