For a Web-based open and dynamic learning environment, personalized support for learners becomes more important. In order to achieve optimal efficiency in a learning process, individual learner's cognitive learning style should be taken into account. Due to different types of learners using these systems, it is necessary to provide them with an individualized learning support system. A framework of cognitive based adaptive Web-based learning support system (WLSS) is presented by focusing on learner's cognitive learning process and activities, as well as the technology support needed. Based on the learner-centered mode and cognitive learning theory, we demonstrate an online course design and development that supports the students with the learning flexibility and the adaptability. The proposed framework utilizes knowledge structure map for representing a dynamic cognitive learning process to support students' deep learning, efficient tutoring and collaboration in Web-based learning environment.