Up to the present, the functions of LMS have been concentrated on showing the learning contents and managing the progress of learning and evaluation for each learner. Viewed in a learner\'s light, most of the existing LMS has a limit not to utilize the character of web based education which is for improvement in the self-directed and cooperative learning abilities. Overcoming the limit of LMS, therefore, the purpose of this study was to build the basic model of compound CAT learning system with practical use of CAT, multimedia, co-teaching, and self-initiative learning contract. The compound CAT developed from this study is a learning system to solve a question arisen in the process of learning for accomplishment of the learning contract settled by learners through collaborative learning of co-teaching method. This system is totally different from passive LMS which is only to carry the contents on the learning web site and wait for learners to study themselves. The compound CAT learning system was designed to make vigorous learning activities possible through progressive participation and cooperation with colleagues from the level of learning planning. In addition to it, this system helps learners choose the contents and evaluation process for themselves, and supports adaptive learning for the learners\' characters and abilities.