PARP (poly ADP-ribose polymerase) family is a crucial DNA repair enzyme that responds to DNA damage, regulates apoptosis, and maintains genome stability; therefore, PARP inhibitors represent a promising therapeutic strategy for the treatment of various human diseases including COVID-19. In this study, a multi-task FP-GNN (Fingerprint and Graph Neural Networks) deep learning framework was proposed to predict the inhibitory activity of molecules against four PARP isoforms (PARP-1, PARP-2, PARP-5A, and PARP-5B). Compared with baseline predictive models based on four conventional machine learning methods such as RF, SVM, XGBoost, and LR as well as six deep learning algorithms such as DNN, Attentive FP, MPNN, GAT, GCN, and D-MPNN, the evaluation results indicate that the multi-task FP-GNN method achieves the best performance with the highest average BA, F1, and AUC values of 0.753 ± 0.033, 0.910 ± 0.045, and 0.888 ± 0.016 for the test set. In addition, Y-scrambling testing successfully verified that the model was not results of chance correlation. More importantly, the interpretability of the multi-task FP-GNN model enabled the identification of key structural fragments associated with the inhibition of each PARP isoform. To facilitate the use of the multi-task FP-GNN model in the field, an online webserver called PARPi-Predict and its local version software were created to predict whether compounds bear potential inhibitory activity against PARPs, thereby contributing to design and discover better selective PARP inhibitors.