Background: Protein-protein interactions (PPIs) are essential to most biological processes. Since bioscience has entered into the era of genome and proteome, there is a growing demand for the knowledge about PPI network. High-throughput biological technologies can be used to identify new PPIs, but they are expensive, time-consuming, and tedious. Therefore, computational methods for predicting PPIs have an important role. For the past years, an increasing number of computational methods such as protein structure-based approaches have been proposed for predicting PPIs. The major limitation in principle of these methods lies in the prior information of the protein to infer PPIs. Therefore, it is of much significance to develop computational methods which only use the information of protein amino acids sequence. Results: Here, we report a highly efficient approach for predicting PPIs. The main improvements come from the use of a novel protein sequence representation by combining continuous wavelet descriptor and Chou's pseudo amino acid composition (PseAAC), and from adopting weighted sparse representation based classifier (WSRC). This method, cross-validated on the PPIs datasets of Saccharomyces cerevisiae, Human and H. pylori, achieves an excellent results with accuracies as high as 92.50%, 95.54% and 84.28% respectively, significantly better than previously proposed methods. Extensive experiments are performed to compare the proposed method with state-of-the-art Support Vector Machine (SVM) classifier. Conclusions: The outstanding results yield by our model that the proposed feature extraction method combing two kinds of descriptors have strong expression ability and are expected to provide comprehensive and effective information for machine learning-based classification models. In addition, the prediction performance in the comparison experiments shows the well cooperation between the combined feature and WSRC. Thus, the proposed method is a very efficient method to predict PPIs and may be a useful supplementary tool for future proteomics studies.