In learning an embodied agent executing daily tasks via language directives, the literature largely assumes that the agent learns all training data at the beginning. We argue that such a learning scenario is less realistic, since a robotic agent is supposed to learn the world continuously as it explores and perceives it. To take a step towards a more realistic embodied agent learning scenario, we propose two continual learning setups for embodied agents; learning new behaviors (Behavior Incremental Learning, Behavior-IL) and new environments (Environment Incremental Learning, Environment-IL) For the tasks, previous ‘data prior’ based continual learning methods maintain logits for the past tasks. However, the stored information is often insufficiently learned information and requires task boundary information, which might not always be available. Here, we propose to update them based on confidence scores without task boundary information (i.e., task-free) in a moving average fashion, named Confidence-Aware Moving Average (CAMA). In the proposed challenging Behavior-IL and Environment-IL setups, our simple CAMA outperforms prior arts in our empirical validations by noticeable margins.