Although there has been much work on the logical formulation of intention, only little attention has been paid on the close relationship between intentions and preferences of an agent. As a result, the previous work cannot properly treat reasoning with information about preferences. In this paper, we investigate a preference-based approach to the logic of intention. Based on an intuition that intentions are desirable choices of an agent, we define a notion of intention in terms of the preference order of an agent. The definition is a simple and intuitive one, and intentions satisfy good and interesting properties. Then we apply our logic to the intention recognition problem. Based on our preference-based definition of intention, we give several sufficient conditions on preferences of an agent under which the action-effect heuristic rule is valid. In this way, we demonstrate that our formalism can give a good basis for designing and understanding heuristics and control strategies for them in the intention recognition domain.