This paper presents a novel method to control humanoid robot dynamic loco-manipulation with multiple contact modes via multi-contact Model Predictive Control (MPC) framework. The proposed framework includes a multi-contact dynamics model capable of capturing various contact modes in loco-manipulation, such as hand-object contact and foot-ground contacts. Our proposed dynamics model represents the object dynamics as an external force acting on the system, which simplifies the model and makes it feasible for solving the MPC problem. In numerical validations, our multi-contact MPC framework only needs contact timings of each task and desired states to give MPC the knowledge of changes in contact modes in the prediction horizons in loco-manipulation. The proposed framework can control the humanoid robot to complete multi-tasks dynamic loco-manipulation applications such as efficiently picking up and dropping off objects while turning and walking.