Learning-outcome prediction (LOP) is a long-standing and critical problem in educational routes. Many studies have contributed to developing effective models while often suffering from data shortage and low generalization to various institutions due to the privacy-protection issue. To this end, this study proposes a distributed grade prediction model, dubbed FecMap, by exploiting the federated learning (FL) framework that preserves the private data of local clients and communicates with others through a global generalized model. FecMap considers local subspace learning (LSL), which explicitly learns the local features against the global features, and multi-layer privacy protection (MPP), which hierarchically protects the private features, including model-shareable features and not-allowably shared features, to achieve client-specific classifiers of high performance on LOP per institution. FecMap is then achieved in an iteration manner with all datasets distributed on clients by training a local neural network composed of a global part, a local part, and a classification head in clients and averaging the global parts from clients on the server. To evaluate the FecMap model, we collected three higher-educational datasets of student academic records from engineering majors. Experiment results manifest that FecMap benefits from the proposed LSL and MPP and achieves steady performance on the task of LOP, compared with the state-of-the-art models. This study makes a fresh attempt at the use of federated learning in the learning-analytical task, potentially paving the way to facilitating personalized education with privacy protection.