The purpose of the study is to identify the effects of the types of concept map on the degree of the academic achievement by learner's cognitive styles under the hypermedia learning environment. To achieve the purpose of the study, the hypotheses were set as follows: 〈Hypothesis Ⅰ〉 There would be a significant difference in academic achievement according to the types of concept map for the learner with reflective cognitive style under the hypermedia learning environment. 〈Hypothesis Ⅱ〉 There would be a significant difference in academic achievement according to the types of concept map for the learner with impulsive cognitive style under the hypermedia learning environment. For the experiment to verify the hypotheses, 260 of the 1st grade students were sampled from 8 classes of I middle school in Seoul. They were randomly assigned to one of the four different experimental groups according to the type of concept map: global-explicit map, local-explicit map, global-embedded map, and local¬embedded map based on the range of the concept display and the type of proposition presentation, explaining the relation of each concept. Each group was treated with the each type of four hypermedia programs, which were developed for the study about the science subject by the researcher. The programs were different from one another in terms of the type of concept map as a navigational tool. The students were allowed to learn the program 3 times (45 minutes each time) and then they were asked 20 questions measuring the degree of the academic achievement. To identify cognitive styles, that is reflective-cognitive style and impulsive-cognitive style, all the students were tested by MFFT(Matching Familiar Figures Test) developed by Kagan(964). The final students for the analysis of the study were 101 with reflective cognitive styles and 104 with impulsive cognitive styles. The results of the study were as follows: 1) 〈Hypothesis 1〉 was rejected. That is to say, there was no significant difference in academic achievement among the four experimental groups for the learners with the reflective cognitive style(p＞ .05). 2) 〈Hypothesis 2〉 was accepted. That is to say, there was no significant difference in academic achievement among the four experimental groups for the learners with the reflective cognitive style(p＜.05). In conclusion, the effects of using the concept map as a navigational tool in the hypermedia learning program depend on the learners' cognitive style. In other words, it can be implied that learners with a reflective cognitive style are hardly affected by the type of concept map on the academic achievement, but learners with an impulsive cognitive style are affected by the type of concept map on the academic achievement under the hypermedia learning environment. Especially in using the embedded concept map, there are negative effects to the achievement scores for learners with an impulsive cognitive style.