This paper presents a new algorithm called competency-based guided-learning algorithm (CBGLA), which can be applied on adaptively guiding e-learning. Computational process analysis and mathematical derivation of competency-based learning (CBL) were used to develop the CBGLA. The proposed algorithm could generate an effective adaptively guiding learning path in order that it would guide the learners to study adaptively without requiring teacher involvement. In order to verify the effectiveness for the CBGLA, a system is implemented. Using statistical methods, the data of which are collected from the students' learning activities on the system, we have verified the efficiency of the CBGLA by the comparison of the pre-test and post-test scores of students. While the learning materials possess fixed scope and could be classified into several categories, students could even learn more effective under the guidance of CBGLA system than a teacher. Analyzing the questionnaire, it also has been shown that learners were very satisfied with the design of the system user interface and the guided-learning mechanism.