This paper aims to investigate academic journal evaluation through the integer DEA (Data envelopment analysis) method. By including expert-based and citation-based journal ranking indicators such as the ABS Ranking, UT/DALLAS list, IF (impact factor), H-index and Eigenfactor score, and considering the first two sequencing expert-based journal ranking indicators and H-index are integer data, this study constructed an integer DEA model to evaluate academic journals in the field of management science and operations research. An indicator is also introduced as input to punish mismanagement of journals by judging whether the self-citation rate is too high. Based on the calculation of our model, four main conclusions are reached. First, the integer DEA model could be a useful method to amend the deviation caused by ignoring integer data and integrate indicators based on expert and citations. Second, by introducing expert-based journal ranking indicators, better results can be obtained when identifying the most important journals; and by introducing citation-based journal ranking indicators, the subjective bias caused by experts’ difficulty in familiarizing with all journals can also be avoid to some extent. Third, by introducing the Cost indicator measured by excessive self-citation rate, we identify the cost of mismanagement by journal editorial board and punish them in DEA score. Last but not the least, we proposed that CRS is more suitable in academic journal evaluation than VRS because there is no effect of increasing or decreasing returns to scale in the process of journal publication and citation. In summary, our integer DEA model is feasible and could be used by universities to form suitable journal ranking list.