We propose a novel computational method known as RVM-LPQ that combines the Relevance Vector Machine (RVM) model and Local Phase Quantization (LPQ) to predict PPIs from protein sequences. The main improvements are the results of representing protein sequences using the LPQ feature representation on a Position Specific Scoring Matrix (PSSM), reducing the influence of noise using a Principal Component Analysis (PCA), and using a Relevance Vector Machine (RVM) based classifier. We perform 5-fold cross-validation experiments on Yeast and Human datasets, and we achieve very high accuracies of 92.65% and 97.62%, respectively, which is significantly better than previous works. To further evaluate the proposed method, we compare it with the state-of-the-art support vector machine (SVM) classifier on the Yeast dataset. The experimental results demonstrate that our RVM-LPQ method is obviously better than the SVM-based method. The promising experimental results show the efficiency and simplicity of the proposed method, which can be an automatic decision support tool for future proteomics research.