The present work aims to solve the problems that the traditional educational administration management system has, such as low efficiency in analyzing big data, and the analysis results have low value, which is based on manual rules definition in big data analysis and processing. The work proposes a student achievement prediction model FCM-CF based on Fuzzy C-means (FCM) and Collaborative Filtering (CF). The work also introduces it into the research of educational administration management to construct an intelligent educational administration management system. At the beginning, the FCM-CF model is described in detail. Then, the system requirements and specific design methods are described in detail. Eventually, with the students’ performance prediction as an example, the performance of the system is tested by designed simulation experiments. The result shows that the students’ achievement in study is closely related to their daily study performance such as preparation before class, classroom performance, attendance, extracurricular study, and homework completion. Generally, the examination scores of students are significant to their daily performances. Under the same experimental conditions, the prediction error of the FCM-CF model proposed here is less than 10.8% of that of other algorithms. The model has better prediction performance and is more suitable for the prediction of middle school students’ examination scores in educational administration management system. The innovation of intelligent educational administration management system is that, in addition to the basic information management function, it also has two other functions: students’ performance prediction analysis and teacher evaluation prediction. It can provide data support for improving teaching quality. The research purpose is to provide important technical support for more intelligent educational administration and reduce the loss of human resources in educational administration.