Learning to adapt to a series of different goals in visual navigation is challenging. In this work, we present a model-embedded actor-critic architecture for the multi-goal visual navigation task. To enhance the task cooperation in multi-goal learning, we introduce two new designs to the reinforcement learning scheme: inverse dynamics model (InvDM) and multi-goal co-learning (MgCl). Specifically, InvDM is proposed to capture the navigation-relevant association between state and goal, and provide additional training signals to relieve the sparse reward issue. MgCl aims at improving the sample efficiency and supports the agent to learn from unintentional positive experiences. Extensive results on the interactive platform AI2-THOR demonstrate that the proposed method converges faster than state-of-the-art methods while producing more direct routes to navigate to the goal. The video demonstration is available at: https://youtube.com/channel/UCtpTMOsctt3yPzXqe_JMD3w/videos.