Humanoid robots are capable of imitating most human actions due to their joint configuration being similar to that of human. Research on motion planning for humanoid robots often focuses on the legs, aiming to plan legs’ trajectories to achieve movements such as walking, running, and jumping. However, when humanoid robots operate in real human environments, relying solely on foot-end contact is often insufficient due to the complexity of the environment. Multi-contact trajectory planning greatly expands the working space of humanoid robots, enabling them to confidently navigate complex environments. To plan multi-contact and whole-body motions for humanoids, we explore a trajectory optimization framework and incorporate relaxed contact constraints to ensure that the solver can find feasible solutions. We introduce a full-body dynamic model for humanoid robots and simplified it into a multi-link model. During the planning process, collision points for the robot are pre-specified, and the kinematics and dynamics of these collision points are derived. The relaxed contact constraints reconcile the conflict between contact forces and contact distances while ensuring the continuity of contact dynamics. We demonstrate that this algorithm is capable of generating multi-contact motion plans with a humanoid robot. In real experiments, humanoid robot BHR-FCR achieve multi-contact motion on flat terrain.