This paper studies a novel trajectory tracking guidance law for a quadrotor unmanned aerial vehicle (UAV) with obstacle avoidance based on nonlinear model predictive control (NMPC) scheme. By augmenting a reference position trajectory to a reference dynamical system, the authors formulate the tracking problem as a standard NMPC design problem to generate constrained reference velocity commands for autopilots. However, concerning the closed-loop stability, it is difficult to find a local static state feedback to construct the terminal constraint in the design of NMPC-based guidance law. In order to circumvent this issue, the authors introduce a contraction constraint as a stability constraint, which borrows the ideas from the Lyapunov’s direct method and the backstepping technique. To achieve the obstacle avoidance extension, the authors impose a well-designed potential field function-based penalty term on the performance index. Considering the practical application, the heavy computational burden caused by solving the NMPC optimization problem online is alleviated by using the dynamical adjustment of the prediction horizon for the real-time control. Finally, extensive simulations and the real experiment are given to demonstrate the effectiveness of the proposed NMPC scheme.