In this paper, a new L1 adaptive back-stepping controller based on the barrier Lyapunov function (BLF) is proposed to respect the position and velocity constraints usually imposed in designing Euler-Lagrange systems. The purpose of this investigation is to improve different aspects of a conventional L1 adaptive control. More specifically, the modified controller has a lower complexity by removing the low-pass filter from the design procedure. The performance of the controller is also enhanced by having a faster convergence speed and increased robustness against nonlinear uncertainties and disturbances arising in practical applications. The proposed scheme is evaluated on two different Euler-Lagrange systems, i.e. a 6-DOF remotely operated vehicle (ROV) and a single-link manipulator. The results for the new back-stepping design are assessed in both scenarios in terms of settling time, percentage of overshoot, and trajectory tracking error. The results confirm that both tracking and state estimation errors for position and velocity outputs outperform the standard L1 adaptive control technique. The results also demonstrate the high performance of the proposed approach in removing the matched nonlinear time-varying disturbances and dynamic uncertainties and a good trajectory tracking despite the uncertainty on the input gain of the system.