Identifying compound-protein interactions (CPIs) is critical in drug discovery, as accurate prediction of CPIs can remarkably reduce the time and cost of new drug development. The rapid growth of existing biological knowledge has opened up possibilities for leveraging known biological knowledge to predict unknown CPIs. However, existing CPI prediction models still fall short of meeting the needs of practical drug discovery applications. A novel parallel graph convolutional network model for CPI prediction (ParaCPI) is proposed in this study. This model constructs feature representation of compounds using a unique approach to predict unknown CPIs from known CPI data more effectively. Experiments are conducted on five public datasets, and the results are compared with current state-of-the-art (SOTA) models under three different experimental settings to evaluate the model's performance. In the three cold-start settings, ParaCPI achieves an average performance gain of 26.75%, 23.84%, and 14.68% in terms of area under the curve compared with the other SOTA models. In addition, the results of the experiments in the case study show ParaCPI's superior ability to predict unknown CPIs based on known data, with higher accuracy and stronger generalization compared with the SOTA models. Researchers can leverage ParaCPI to accelerate the drug discovery process.