As therapeutic peptides have been taken into consideration in disease therapy in recent years, many biologists spent time and labor to verify various functional peptides from a large number of peptide sequences. In order to reduce the workload and increase the efficiency of identification of functional proteins, we propose a sequence-based model, q-FP (functional peptide prediction based on the q-Wiener Index), capable of recognizing potentially functional proteins. We extract three types of features by mixing graphic representation and statistical indices based on the q-Wiener index and physicochemical properties of amino acids. Our support-vector-machine-based model achieves an accuracy of 96.71%, 92.52%, 98.40%, and 91.40% for anticancer, virulent, and allergenic proteins datasets, respectively, by using 5-fold cross validation.