In this paper, the trajectory tracking problem of unmanned surface vehicles (USVs) with position constraints is investigated. Given that the constrained control design based on barrier Lyapunov functions requires the initial output of the system to satisfy a feasibility condition, a more universal position-constrained solution based on nonlinear mapping strategy is proposed. Then, by combining the backstepping method, neural networks, finite-time control techniques, and input quantization, an adaptive finite-time quantized controller that can achieve a balance between tracking performance and resource conservation is developed. The proposed controller has the advantages of few learning parameters, low update frequency of control input, as well as non-singularity and simplicity. As usual, a complete theoretical stability analysis and numerical simulation are presented at the end.