This paper proposes an intent-aware multi-agent planning framework as well as a learning algorithm. Under this framework, an agent plans in the goal space to maximize the expected utility. The planning process takes the belief of other agents' intents into consideration. Instead of formulating the learning problem as a partially observable Markov decision process (POMDP), we propose a simple but effective linear function approximation of the utility function. It is based on the observation that for humans, other people's intents will pose an influence on our utility for a goal. The proposed framework has several major advantages: i) it is computationally feasible and guaranteed to converge. ii) It can easily integrate existing intent prediction and low-level planning algorithms. iii) It does not suffer from sparse feedbacks in the action space. We experiment our algorithm in a real-world problem that is non-episodic, and the number of agents and goals can vary over time. Our algorithm is trained in a scene in which aerial robots and humans interact, and tested in a novel scene with a different environment. Experimental results show that our algorithm achieves the best performance and human-like behaviors emerge during the dynamic process.