During high-speed atmospheric flight, reentry vehicles are subject to process constraints such as dynamic pressure and heat flux, while also needing to meet terminal constraints including landing position, velocity, and flight path angle. Additionally, these vehicles face both disturbance uncertainties and parametric uncertainties. Consequently, reentry guidance methods must simultaneously satisfy multi-constraint requirements and robustness criteria. This paper proposes a contraction theory based multi-constraint robust guidance method for reentry vehicles. The approach employs convex optimization to solve for the control contraction metric, thereby completing the trajectory-tracking guidance law design. The trajectory tracking errors induced by uncertainties are explicitly solved, and an iterative design process yields a nominal trajectory that meets robustness requirements. Monte Carlo simulations demonstrate that the proposed method can satisfy all multi-constraint conditions within the given uncertainty bounds.