It is significant for biological cells to predict self-interacting proteins (SIPs) in the field of bioinformatics. SIPs mean that two or more identical proteins can interact with each other by one gene expression. This plays a major role in the evolution of proteinprotein interactions (PPIs) and cellular functions. Owing to the limitation of the experimental identification of self-interacting proteins, it is more and more significant to develop a useful biological tool for the prediction of SIPs from protein sequence information. Therefore, we propose a novel prediction model called RP-FFT that merges the Random Projection (RP) model and Fast Fourier Transform (FFT) for detecting SIPs. First, each protein sequence was transformed into a Position Specific Scoring Matrix (PSSM) using the Position Specific Iterated BLAST (PSI-BLAST). Second, the features of protein sequences were extracted by the FFT method on PSSM. Lastly, we evaluated the performance of RP-FFT and compared the RP classifier with the state-of-the-art support vector machine (SVM) classifier and other existing methods on the human and yeast datasets; after the five-fold cross-validation, the RP-FFT model can obtain high average accuracies of 96.28% and 91.87% on the human and yeast datasets, respectively. The experimental results demonstrated that our RP-FFT prediction model is reasonable and robust.