Accurate assessment of protein-protein interactions (PPIs) is critical to deciphering disease mechanisms and developing novel drugs, and with rapidly growing PPI data, the need for more efficient predictive methods is emerging. We propose here a symmetric logistic matrix factorization (symLMF)-based approach to predict PPIs, especially useful for large PPI networks. Benchmarked against two widely used datasets (Saccharomyces cerevisiae and Homo sapiens benchmarks) and their extended versions, the symLMF-based method proves to outperform most of the state-of-the-art data-driven methods applied to human PPIs, and it shows a performance comparable to those of deep learning methods despite its conceptual and technical simplicity and efficiency. Tests performed on humans, yeast, and tissue (brain and liver)- and disease (neurodegenerative and metabolic disorders)-specific datasets further demonstrate the high capability to capture the hidden interactions. Notably, many "de novo predictions" made by symLMF are verified to exist in PPI databases other than those used for training/testing the method, indicating that the method could be of broad utility as a simple, yet efficient and accurate, tool applicable to PPI datasets.