To address the safety challenge of collision avoidance in formation navigation of heterogeneous under-actuated unmanned surface vehicles (USVs), this paper proposes a distributed model predictive trajectory-based collision-free formation control strategy. A formation reference trajectory is generated through the leader–followers scheme, and a distributed nonlinear model predictive control (DNMPC) algorithm is employed to design an accurate formation trajectory tracking controller. A novel dual-constraint mechanism with both hard and soft constraints is introduced: external obstacle avoidance constraints are considered, while the internal collision-avoidance problem is modeled as a time-parameterized nonlinear state constraint based on predicted trajectories, rather than solely on instantaneous positions. This design effectively prevents the risk of excessive proximity among formation members. Finally, input-to-state stability (ISS) of the proposed method is demonstrated by employing a Lyapunov function. Simulations on a three-vessel heterogeneous under-actuated formation demonstrate the effectiveness and reliability of the proposed method in efficient collision avoidance, stable formation-keeping and switching.