We propose a goal-driven approach to model the service request intention in service-oriented systems. The service request intention can be extracted from the user input and modeled by predefined goal models. We identify this problem as the service request intention extraction. If a service-oriented system has the abilities of user's intention extraction and can make some activities to satisfy the extracted intention, the system can provide a more convenient and efficient service for the user. We start the system construction from the view of goal-driven requirements engineering. The requirements specification is generated by the goal-based requirements analysis in which the functional and nonfunctional requirements will be extended with goal models. A set of computable goal models that represent the user requirements is selected and refined as the basis of system services. The designer can also design related system services based on the requirements specification. Based on the proposed intention extraction approach, the user's vague and imprecise intention will be extracted and mapped to computer understandable and computable goal models for representing the intention. A case-based method is developed to implement the intention extraction process. The intention interpretation knowledge is stored in a case base, and the intention interpretation is based on the process of case retrieval and adaptation. A general architecture for an intention-aware service-oriented system is proposed for demonstrating how to apply the proposed approach.