This paper addresses the tracking control problem for uncertain Euler-Lagrange system with time-varying output constraints in an environment containing obstacles. First, a novel log-type attractive potential field is utilized to describe the trajectory tracking task with time-varying constraints, and a bounded artificial potential field is established to describe the obstacle avoidance task. Then, by incorporating the two artificial potential fields (APFs) into the dynamic surface control, a neuro-adaptive tracking control is designed for the uncertain Euler-Lagrange system, which can ensure the system to fulfill the trajectory track task within time-varying limit range while avoiding obstacles. Because the obstacle avoidance task has a higher priority, the proposed control scheme can also guarantee the obstacle avoiding task can be fulfilled first when it is conflicted with the trajectory tracking task. Numerical simulations are provided to demonstrate the efficacy of the control strategy.